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THE  INTERNATIONAL  SCIENTIFIC  SERIES 
VOLUME   LXXIII 


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New  York :    D.  APPLETON  &  CO.,  72  Fifth  Avenue. 


THE   INTERNATIONAL   SCIENTIFIC   SERIES 


MOVEMENT 


BY 

E.   J.    MAEEY 

MEMBER   OF  THE   INSTITUTE   AND   OP  THE   ACADEMY   OF  MEDICIN1 

PROFESSOR  AT   THE    COLLEGE   OF  FRANCE 

DIRECTOR    OF    THE    PHYSIOLOGICAL    STATION 


TRANSLATED    BY 

ERIC  PRITCHARD,  M.A.,  M.B.,  B.Ch.  (Oxon.) 


WITH  TWO  HFXDBED   ILLUSTRATIONS 


NEW    YORK 

D.    APPLETON    AND    COMPANY 

1895 


Authorised  Edition. 


TRANSLATOR'S    NOTE 

Instantaneous  photography,  especially  that  branch 
of  it  known  as  Chronophotography,  has  already  won 
for  itself  a  recognized  position  among  the  methods 
of  scientific  research,  and  in  the  near  future  it  is 
probable  that  it  will  be  even  more  generally  appre- 
ciated. Marey  and  Muybridge  must  undoubtedly  be 
regarded  as  the  two  pioneers  of  the  method ;  the 
works  of  the  latter,  written  in  English  and  published 
in  America,  are  within  the  reach  of  all  who  can  read 
the  English  language ;  on  the  other  hand,  the  works 
of  Marey  are  for  the  most  part  inaccessible  to  those 
who  are  unfamiliar  with  French.  It  is  for  this  reason 
that  I  applied  for  and  obtained  permission  to  translate 
this  work. 

"  Le  lEouvement  "  is  one  of  the  most  recent  and 
important  publications  of  this  eminent  physicist  and 
physiologist,  and  it  is,  I  believe,  the  most  compre- 
hensive summary  hitherto  published,  of  the  results 
and  possibilities  of  instantaneous  photography ;  every 
page  has  its  interest  not  only  for  the  specialist,  but 
also  for  the  general  reader ;  and  further,  the  book  is 
replete  with  suggestiveness  of  new  lines  of  research. 

Chronophotography  is  a  new  subject,  and  many  of 


VI  TRANSLATOR'S  NOTE 

its  technical  terms  are  known  even  to  English  scientific 
men  only  in  their  French  form.  For  these  I  have 
frequently  used  periphrases,  remembering  that  many 
of  my  readers  may  not  be  experts.  I  must  acknow- 
ledge gratefully  the  continued  assistance  of  my  sister, 
Mrs.  Chalmers  Mitchell,  not  only  in  making  the  actual 
translation,  but  in  revising  it  for  the  press. 


EEIC   PEITCHARD. 


14,  Cromwell  Place,  S.W. 
August,  1895. 


PREFACE 

The  graphic  method,  with  its  various  developments, 
has  been  of  immense  service  to  almost  every  branch 
of  science,  and  consequently  many  improvements  have 
of  late  been  effected.  Laborious  statistics  have  been 
replaced  by  diagrams  in  which  the  variations  of  a 
curve  express  in  a  most  striking  manner  the  several 
phases  of  a  patiently  observed  phenomenon,  and, 
further,  a  recording  apparatus  which  works  automati- 
cally can  trace  the  curve  of  a  physical  or  physiological 
event,  which  by  reason  of  its  slowness,  its  feeble- 
ness, or  its  rapidity,  is  otherwise  inaccessible  to 
observation.  Sometimes,  however,  a  curve  which 
represents  the  phases  of  a  phenomenon  is  found  so 
misleading  that  another  and  more  serviceable  method, 
namely,  that  of  chronophotography,  has  been  invented. 
The  development  of  these  new  methods  of  analyzing 
movement  could  never  have  proceeded  within  the 
confined  space  of  a  physiological  laboratory.  For 
instance,  in  comparing  the  locomotion  of  various 
species  of  animals,  it  is  essential  that  each  should 
be  studied  under  natural  conditions :  fish  in  fresh 
water  or  marine  aquariums ;  insects  in  the  open  air ; 
and  man,  quadrupeds,  and  birds  in  wide  spaces  in 
which  their  movements  are  unfettered. 


Vlll  PREFACE 

The  Physiological  Station,  endowed  by  the  State 
and  the  City  of  Paris,  has  afforded  in  this  respect 
unique  opportunities,  and  there,  with  new  appliances, 
the  following  investigations  have  been  for  the  most 
part  carried  out. 

We  shall  see  by  a  variety  of  instances  to  what  ex- 
tent the  older  methods  are  applicable  for  the  analysis 
of  certain  phenomena,  and  what  progress  has  been 
achieved  by  chronophotography. 

Each  chapter  is  nothing  more  than  an  outline,  for 
any  attempt  to  fill  in  the  details  of  any  section  would 
monopolize  the  time  and  attention  of  a  trained 
specialist. 

In  a  few  instances  such  an  attempt  has  been  made,  for 
geometricians,  hydraulic  engineers,  naval  and  military 
men  as  well  as  artists  have  all  had  recourse  to  this 
method,  and  at  last  naturalists  have  interested  them- 
selves in  the  matter.  It  is  more  especially  to  this 
latter  class  that  we  dedicate  our  work,  since  it  appeals 
to  their  particular  ambition,  namely,  that  of  discover- 
ing among  the  phenomena  of  life  something  that  has 
hitherto  escaped  the  most  attentive  observation. 


CONTENTS 


CHAPTER  I 

TIME 

Its  Graphic  Record  ;  Time-measurement  by  means  of  Photography 

PAGE 

Summary. — Graphic  record  of  time— Chronography— Rudiments 
of  the  method — Transmission  of  movement  to  the  recording 
needle  which  registers  the  duration — L'hronographic  record 
of  a  man's  foot  in  walking,  during  the  phases  of  rest  and 
motion — The  same  of  the  four  feet  of  a  horse  in  its  various 
paces — Record  of  the  fingering  of  a  pianist — Applications 
of  photography  to  the  registration  of  time  -Measurement  of 
the  exposure  allowed  by  a  photographic  shutter — Measure- 
ment of  the  time  intervals  between  successive  exposures      .         1 


CHAPTER  II 

SPACE 
Its  Measurement  and  Representation  by  Photography 

Summary. — Tendency  to  replace  outline  drawings,  plans,  and 
diagrams  in  relief  by  photography — Photography  traces  the 
various  positions  in  space  occupied  by  a  moving  body  — 
Photographic  trajectory  of  the  movements  of  a  point  in 
space ;  its  stereoscopic  trajectory — Movements  of  a  straight 
line  in  space — Solid  figures  formed  thereby :  cylinders, 
hyperboloids,  cones,  etc. — Movements  of  a  curve  in  space  ; 
photography  of  the  figures  which  it  forms :  spheres,  ellip- 
soids, etc. — Stereoscopic  pictures  of  figures  of  three  dimen- 
sions— Figures  formed  by  the  movement  of  solid  bodies; 
effects  of  light  and  shade 18 


CONTENTS 


CHAPTER  III 


MOVEMENT 

Its  Measurement,  Graphic  Representation,  and  Analysis  by 
means  of  chronophotography 

PAGE 

Summary. — The  understanding  of  a  movement  implies  a  double 
knowledge,  namely,  that  of  space  as  well  as  that  of  time — 
Graphic  representation  of  a  movement — Chart  of  a  train 
travelling  along  a  l.ne — The  curve  of  a  prolonged  movement 
should  be  recorded  in  sections — How  a  moving  body  can 
record  its  own  movement — Proportional  enlargement  and 
reduction  of  the  recorded  movement — Odography — Photo- 
graphic record  of  movement — Photography  of  the  movement 
of  Lippmann's  electrometer — Determination  by  means  of 
chronophotography  of  the  movements  executed  by  ;i  falling 
body — Construction  of  the  curves  of  movement  from  clirono- 
photographic  images — Time-curve  of  the  distance  traversed 
— Curve  of  velocity — Curve  of  acceleration     .         .         .         .33 


CHAPTER  IV 

CHRONOPHOTOGRAPHY  ON  FIXED  PLATES 

Summary. — Object  of  chronophotography;  principles  of  the 
method ;  measurement  of  time  and  space — Influence  of  the 
extent  of  surf.ice  covered  by  the  object  which  is  to  be  photo- 
graphed ;  influence  of  the  rate  of  movement— Geometrical 
chronophotography  —  Stereoscopic  chronophotography  — 
Method  of  multiplying  the  number  of  images  without  pro- 
ducing confusion— Alternating  images — Separation  of  the  • 
images  ou  the  photographic  plate;  separation  by  moving  the 
apparatus — Separation  by  employing  a  revolving  mirror       .       54 


CHAPTER  V 

DESCRIPTION    OF    THE    APPARATUS 

Summary. — Construction  of  the  apparatus— Slide,  object-glass, 
circular  diaphragms — Erection  of  the  dark  background  at 
the  physiological  station — Dark  background  for  p.ioto- 
grapning  objects  in  water — Photography  of  light  objects  in 
darkne.-s  or  in  a  red  light — Colour  of  objects,  and  way  of 
illuminating  them — Disposition  and  preparation  of  the  dark 
field — Choi  ,«•  of  the  object-glass — Focussing — How  to  take 
the  photographs 67 


CONTENTS  XI 

CHAPTEE  VI 

APPLICATIONS    OF    CHRONOPHOTOGRAPHY    TO    MECHANICS 

PAGE 

Summary. — Bodies  falling  in  air — Ballistic  experiments — The 
resistance  of  the  air  to  surfaces  variously  inclined — Applica- 
tions of  chronophotography  to  hydrodynamics — Fluid  veins  ; 
changes  in  shape  of  fluid  waves ;  intrinsic  movements  of 
fluid  waves — Currents  and  el  dies— Influence  of  the  shape 
of  bodies  placed  in  currents — Oscillations  and  vibrations — 
Rolling  of  ships — Vibrations  of  metal  bridges       ...       84 

CHAPTER  VII 

CHRONOPHOTOGRAPHY    ON    MOVING    PLATES 
Principles  and  History  of  the  Method 

Summary. — Janssen's  astronomical  revolver — Muy bridge's  ex- 
periments :  luminous  background — Photographic  cameras  ar- 
ranged in  series — Control  of  the  instantaneous  shutter  by 
electrical  means — Photographic  gun — Internal  structure  of 
the  instrument  -  Method  of  changing  the  photographic  plates 
— Principles  of  chronophotography  on  moving  plates— Em- 
ployment of  chronophotography — Necessity  for  arresting  the 
progress  of  the  film  at  th«  moment  of  exposure — Moment  to 
choose  for  taking  the  photograph — Form  and  dimensions 
of  the  photographs — Regulation  of  the  number  and  dimen- 
sions of  the  photographs — Reproduction,  enlaigement,  and 
reduction  of  chronuphotographs 103 


CHAPTER  VIII 

HUMAN     MOVEMENTS 

From  the  Point  of  View  of  Kinetics 

Summary. — Some  movements  in  man;  the  study  of  them  by  the 
graphic  method — Speed  of  different  paces  in  man ;  relation- 
ship between  the  frequency  and  length  of  stride — Duration 
of  the  rise  and  fall  of  the  foot  in  walking  and  running — 
Path  described  by  any  particular  part  of  the  body  during 
different  paces ;  mechanical  means  of  recording  it — The 
study  of  movements  in  man  by  means  of  chronophotography 
on  fixed  plates  ;  long-jumping ;  high-jumping — Skilled  move- 
ments, fencing,  etc. — Jumping  from  a  height — The  swing  of 
the  leg  in  walking 126 


Xll  CONTENTS 


CHAPTER  IX 

CERTAIN    MOVEMENTS   IN    MAN 

From  the  Point  of  View  of  Dynamics 

PAGE 

Summary. — Object  of  dynamics  —  Measurement  of  the  forces 
which  play  a  part  in  human  locomotion — Traction  dynamo- 
graph — Dynamograph  for  expressing  the  amount  of  pressure 
exercised  by  the  feet  on  the  ground — Combination  of  the 
dynamograph  with  a  method  of  recording  movements — The 
laws  of  ballistics  as  applied  to  the  mechanism  of  jumping — 
Combined  employment  of  dynamography  and  chronophoto- 
graphy — Mechanical  work  done  in  human  locomotion ;  work 
in  the  vertical  direction;  work  in  the  horizontal  direction; 
work  done  in  maintaining  the  movement  of  the  lower  limbs 
during  their  period  of  suspension — Relative  amount  of  work 
done  during  different  kinds  of  paces — Practical  applications     146 


CHAPTER  X 

LOCOMOTION    IN    MAN 

From  an  Artistic  Point  of  View 

Summary.  — Influence  of  Photography  on  Art— Different  cha- 
racteristics of  ancient  and  modern  works  of  art — Photo- 
graphy catches  the  real  attitude — Importance  of  representing 
the  correct  outline  of  muscles  during  different  actions — 
Photographs  taken  from  different  points  of  view — Photo- 
graphs taken  from  above — Study  of  the  most  characteristic 
attitudes  in  a  movement— Importance  of  having  a  series 
of  photographs  from  which  to  choose  the  most  expressive 
attitude — Analysis  of  facial  expression — Choice  of  the  best 
method  for  procuring  artistic  results 1G9 


CHAPTER  XI 

LOCOMOTION    OF    QUADRUPEDS 

Summary. — Chronography  shows  how  the  feet  rise  and  fall  in 
the  different  paces  of  a  horsi — Transition  or  passage  from 

one  pace  i nother     Representation  of  the  attitudes  in  all 

paces  of  a  horse,  as  shown  by  chronography  and  hoof-marks 


CONTENTS  Xlll 


PAGE 


— Comparison  between  diagrams  obta'ned  bv  these  methods 
and  those  obtained  by  instantaneous  photography — Chrono- 
photography  applied  to  the  representation  of  a  horse  in 
motion — Artistic  representation  of  the  horse  among  the 
ancients — Locomot  on  of  the  horse  from  the  physiological 
point  of  view — Geometrical  chronophotography  of  the  move- 
ments taken  as  a  whole— Individual  movements  of  the  foot 
and  fetlock 186 


CHAPTER  XII 

LOCOMOTION    IN    WATER 

Summary. — Different  types  of  loeomotmn  in  water — Method  of 
photographing  aquatic  animals — Jelly  fish:  Cornatula* — 
Locomotion  by  means  of  undulatory  nnd  lateral  movements  ; 
the  eel — best  arrangement  for  studying  its  movements — 
Locomotion  by  means  of  undulatory  and  vertical  movements; 
the  skate — special  arrangement  for  studying  its  vertical  un- 
dulations from  different  points  of  view— Undulatory  move- 
ments of  the  skate  as  seen  from  the  side :  ditto  as  seen 
from  in  front — The  sea-horse  :  the  fresh- water  tortoise — 
Slow  movements  of  star-fish  —  Lncomoti<  n  of  small  marine 
animals 211 


CHAPTER  XIII 

AERIAL     LOCOMOTION 

The  Flight  of  Birds 

Si  mmary. — Borelli's  theory  on  the  mechanism  of  the  flight  of 
birds  — Chronography  u>ed  for  determining  the  frequency 
of  the  movements  of  the  wing,  and  the  relative  dura- 
tion of  the  rise  and  fall — Myography — Method  of  record- 
ing the  phases  of  contraction  and  relaxation  of  the  wing 
muscles — Record  of  the  trajectory  of  a  bird's  humerus,  and 
the  variations  in  inclination  of  the  surface  of  the  wing — 
Pii olographic  trajectory  of  the  tip  of  the  wing — Chroi.o- 
photography  as  showing  the  successive  attitudes  of  the  bird 
during  the  different  phases  of  movement  of  the  wings — 
Photographs  of  hirds  taken  from  different  aspects — Simul- 
taneous chronophotographv 226 

2 


XIV  CONTENTS 

CHAPTER  XIV 

AERIAL    LOCOMOTION 
The  Flight  of  Insects 

Summauy. — Frequency  of  the  movements  of  insects'  wings  as 
estimated  by  the  sound  produced  in  flying — Mechanical  re- 
gistration of  the  movements  of  the  wings;  frequency  among 
different  species — Synchronous  movements  of  the  wings — 
Changes  in  inclination  of  the  win-j;  surface — Trajectory  of 
in  insect's  wing — Its  interpretation — Experiments  to  de- 
monstrate the  direction  of  movement  of  the  wing,  and  its 
variations  in  piane — The  artificial  insect — Theory  of  the 
flight  of  insects — Photography  as  applied  to  the  study  of 
insect  flight — Lendenfeld's  experiments — Trajectory  of  the 
wing  as  the  insect  advances — Photography  on  moving  films 
— Arrangement  of  the  experiment — Different  types  of  flying 
insects :  Bees,  flies,  tipulce-  Substantiation  of  the  mechanical 
theory  of  flight 


CHAPTER  XV 

COMPARATIVE   LOCOMOTION 

Summary. — Comparative  locomotion  among  terrestrial  mammals: 
the  man,  the  horse,  the  elephant — Comparative  locomotion 
among  different  kinds  of  birds— Classification  of  different 
types  of  locomotion-  Comparative  locomotion  of  tortoises 
and  lizards ;  frogs,  toads,  and  tadpoles ;  snakes,  eels,  and 
fish  ;  insects  and  spiders 258 


CHAPTER  XVI 

APPLICATIONS    OF    CHRONOPHOTOGUAPHY    TO    EXPERIMENTAL 
PHYSIOLOGY 

Soimary. — Numerous  applications  of  chronophotography ;  it 
supplements  the  information  derived  from  the  graphic 
method — Study  of  the  movements  of  the  heart  by  means  of 
the  graphic  method — Photography  of  the  successive  phases 
of  cardiac  action  in  a  tortoise  under  conditions  of  artificial 
circulation — Variations  in  shape  and  capacity  of  the  auricles 
and  ventricles  during  a  cardiac  cycle-- Mechanism  of  car- 
diac pulsation  studied  by  means  of  chronophotography — 
Comparative  advantages  of  mechanical  and  chronophoto- 
graphic  registration — Determination  of  the  centres  of  move- 
ments in  joints 275 


CONTENTS  XV 


CHAPTER  XVII 

MICROSCOPIC    CHRONOPHOTOGRAPHY 

PAG  R 

Summary. — Various  movements  observable  within  the  field  of 
the  microscope — Applications  of  chronophotography  to  the 
study  of  these  movements — Difficulties  of  the  subject — 
Special  arrangement  of  the  apparatus  for  chronophotography 
on  rixed  plates  and  on  moving  films — Retraction  of  the  stalk 
in  vorticella — M  ivement  of  the  blood  in  capillary  vessels — 
Movements  of  the  zoospores  in  the  cells  of  conferva — The 
use  of  the  solar  microscope  in  chronophotography — The  easy 
application  of  this  method 291 


CHAPTER  XVIII 

SYNTHETIC   RECONSTRUCTION   OF   THE   ELEMENTS    OF    AN 
ANALYZED    MOVEMENT 

Summary.  — Plateau's  method;  his  phenakistoscope — The  zoo- 
trope;  its  applications  to  the  study  of  horses'  paces  and 
their  relations  to  one  another— The  use  of  instantaneous 
photography  in  connecti  n  with  the  zootrope — Muybridge, 
Anschiitz — Scientific  app.ications  of  Plateau's  method — 
Points  of  a  good  apparatus— Improvements  made  by  diffe- 
rent authors  —  Attempts  at  constructing  a  chronophoto- 
graphic  projector 301 

Index 319 


MOVEMENT 

CHAPTER  I 

TIME 

Its  Graphic  Record  ;  Time-measurement  by  means 
of  Photography 

Summary. — Graphic  record  of  time— Chronograph}- — Rudiments  of 
the  method — Transmission  of  movement  to  the  recording  needle 
which  registers  the  duration — Chronographic  record  of  a  man's 
foot  in  walking,  during  the  phases  of  rest  and  motion — The  same 
of  the  four  feet  of  a  horse  in  its  various  jiaces — Record  of  the 
fingering  of  a  pianist--Applicalions  of  photography  to  the  regis- 
tration of  time — Measurement  of  the  exposure  allowed  by  a  photo- 
graphic shutter — Measurement  of  the  time  intervals  between 
successive  exposures. 

Graphic  Record  of  Time. — Time,  like  other  magni- 
tudes, can  be  represented  in  a  graphic  form  by  straight 
lines  of  various  lengths.  In  this  way  the  respective 
duration  of  several  events  can  be  gauged  by  the 
various  lengths  of  parallel  straight  lines  placed  side  by 
side.  The  order  of  commencement  of  these  phenomena 
can  be  expressed  by  the  relative  positions  of  the  begin- 
nings of  the  straight  lines.  With  regard  to  the  exact 
order  and  duration  of  the  events,  they  can  be  indicated 
bv  means  of  a  scale,  subdivided  into  divisions  which 


MOVEMENT 


represent   years,   days,   or   fractions   of    seconds.      A 
diagram  will  elucidate  this  method  of  time-measure- 


B 

C  — 


1       i       2      I       3      |       4       j       5      I       6       1       7       J      8      1 


Fig.  1 Scale  of  hours.     Time  measurement. 

ment.  Suppose  we  require  to  express  the  order  and 
sequence  of  three  events,  A,  B,  C,  which  occur 
during  a  period  of  11  hours.  Their  respective  time 
relations  are  expressed  most  clearly  by  the  three  lines 
A,  B,  C,  and  by  the  scale  of  hours  which  accompanies 
them.  It  may  be  seen  by  a  glance  at  the  diagram 
that  the  event  A  commences  at  2  o'clock  and  finishes 
at  10  o'clock  (its  total  duration  is,  therefore,  8 
hours) ;  that  B,  commencing  at  6  and  ending  at 
11  o'clock,  has  lasted  5  hours;  and  that  C,  com- 
mencing at  5  o'clock  and  ending  at  a  £  past  8,  has 
only  extended  over  a  period  of  3^  hours.  The 
sequence  of  these  events  is  accurately  expressed  by 
the  divisions  on  the  scale,  which  correspond  to  the 
beginnings  of  the  different  lines. 

Language  is  as  slow  and  obscure  a  method  of  ex- 
pressing  the  duration  and  sequence  of  events  as  the 
graphic  method  is  lucid  and  easy  to  understand.  As  a 
matter  of  fact,  it  is  the  only  natural  mode  of  expressing 
such  events ;  and,  further,  the  information  which  this 
kind  of  record  conveys  is  that  which  appeals  to  the 
eyes,  usually  the  most  reliable  form  in  which  it  can  be 
expressed.  A  celebrated  English  political  economist, 
W.  Playfair,  has  drawn  up  a  table  of  the  chronological 
order  of  the  reigns  of  the  various  English  sovereigns. 
From  it  one  can  see  at  a  glance  the  age  at  which  each 
succeeded  to  the  throne,  as  well  as  the  duration  of  the 


TIME  3 

reign.  By  the  side  of  this  chronological  table,  another 
series  of  lines  shows  the  succession  of  the  various 
ministers,  and  a  third  shows  the  periods  of  war  and 
peace  occurring  during  the  respective  epochs. 

Such  a  table  expresses  in  the  most  lucid  manner  the 
sequence  of  events.  That  such  a  mode  of  graphic 
record  has  been  neglected  in  France  cannot  be  too 
deeply  deplored*  A  somewhat  similar  method  was 
utilized  in  France  during  the  last  century  to  express 
the  duration  and  sequence  of  certain  acts.  Vincent 
and  Goiffon  *  have  represented  by  a  chronological 
record  the  phases  of  rest  and  motion  of  horses'  feet,  as 
observed  in  their  different  paces.  This  mode  of  ex- 
pression is  surely  preferable  to  that  of  language,  when 
it  is  a  question  of  conveying  to  the  mind  the  meaning 
of  complicated  rhythms. 

Chronography. — The  diagrams  of  which  we  have 
just  been  speaking  are,  however,  only  one  mode  of 
representation,  clearer,  it  is  true,  than  others,  but 
reliable  only  in  so  far  as  the  data  on  which  they 
depend  are  trustworthy.  In  experiments,  for  instance, 
which  deal  with  time  measurements,  it  is  of  immense 
importance  that  the  graphic  record  should  be  auto- 
matically registered,  in  fact,  that  the  phenomenon 
should  give  on  paper  its  own  record  of  duration,  and 
of  the  moment  of  production.  This  method,  in  the 
cases  in  which  it  is  applicable,  is  almost  perfect.  In 
other  instances  photography  comes  to  the  rescue,  and 
affords  accurate  measurements  of  time  events  which 
elude  the  naked  eye.  The  process  which  thus  serves 
to  register  the  duration  and  sequence  of  events  con- 
stitutes a  method  called  "  chronography." 

We  are  about  to  explain  this   method,  proceeding 

*  Memoire  artificielle  des  principesrelatifs  a  la  fidele  representation 
des  nnimaux  tunt  en  peinture  qu'en  sculpture,  par  feu  Goiffon  et 
M.  Vincent.     In-fol.  1779. 


4  MOVEMENT 

from  the  more  simple  to  the  more  complicated  cases. 
We  shall  first  show  how  the  method  can  be  applied  to 
register  the  successive  phases  of  rest  and  motion,  as 
executed  by  a  man's  foot  in  walking,  and  then  the 
movements  of  the  four  feet  of  a  horse  as  they  occur  in 
its  various  paces,  and,  lastly,  the  automatic  method  of 
registering  the  fingering  of  a  pianist  on  the  keys  of 
his  instrument.  This  last  problem  must  be  regarded 
as  one  of  the  most  difficult  to  solve. 

Rudiments  of  Chronography. — Let  us  suppose  that  a 
strip  of  paper  is  made  to  travel  by  clockwork  at  a 
uniform  rate,  and  that  a  pen  fixed  above  the  paper 
marks,  as  it  alternately  rises  and  falls,  the  various 
periods  and  intervals. 

As  the  pen  comes  in  contact  with  the  paper  it  leaves 
its  record  in  the  form  of  "  dashes,"  of  various  lengths, 
and  at  various  intervals ;  and  by  this  means  the 
sequence  and  duration  are  registered.  If  the  "  dashes  " 
are  equidistant,  it  means  that  the  periods  of  contact 
follow  one  another  at  equal  intervals  of  time.  Finally, 
if  it  is  necessary  to  obtain  an  accurate  measurement  of 
the  duration  of  contact,  and  of  the  intervals  between, 
the  exact  rate  at  which  the  strip  of  paper  is  being 
carried  must  be  known.  A  control  record  of  the 
rate  may  be  obtained  by  allowing  the  oscillation  of  a 
pendulum  to  mark  the  seconds  on  the  paper,  or,  if  the 
movement  be  very  rapid,  by  allowing  the  vibrations  of 
a  tuning-fork,  of  which  the  rate  of  vibration  is  known, 
to  trace  themselves  upon  the  paper.* 

Transmission  of  the  Movement  to  the  Recording  Needle 
which  registers  the  Duration, — It  hardly  ever  happens 
that  the  phenomena,  of  which  one  wishes  to  record 
the  sequence  and  duration,  are  capable  of  acting 
directly  on   the  recording   needle.     More  often  such 

*  For  the  jieneral  principles  of  chronography,  its  technique  and 
applications,  see  "The  Graphic  Method,"  pages  133,  142,  456. 


TIME 


5 


movements  have  to  be  observed  at  a  distance  and 
transmitted  to  the  corresponding  recording  needle. 
For  this  purpose  transmission  by  air  is  employed  and 
found  preferable  to  transmission  by  electricity.  The 
following  apparatus  effects  this  object. 

Two  similar  apparatuses  are  coupled  together  by 
pneumatic  connecting  tubes,  and  the  whole  apparatus 
goes  by  the  name  of  "  lever-drums."  *    Each  part  con- 


FiG.  2. — Arrangement  deigned  for  transmitting  a  movement  to  the  needle,  which 
records  the  duration  and  tae  pluses. 


sists  of  a  metal  capsule,  with  a  gutta-percba  membrane 
stretched  over  the  top  ;  a  lever  is  attached  to  the 
membrane  by  means  of  a  jointed  crank.  If  the  first 
lever  is  pulled  by  the  hand  and  lowered,  the  air  in  the 
first  tambour  is  compressed  and  passes  into  the  second, 
the  corresponding  lever  is  raised,  and  reproduces  in  all 
its  phases  the  traction  exercised  on  the  string.     On 

*  Usually  called  "Marpy'a  Tambours,"  in  .England. — Translator. 


6  MOVEMENT 

the  hand  being  released,  the  opposing  force  brings  the 
first  lever  back  into  its  original  position,  the  air 
returns  from  the  second  into  the  first  tambour,  and 
the  lever  of  the  second  falls  in  consequence.  Thus 
the  movements  produced  by  raising  or  lowering  the 
hand  are  transmitted  after  an  inappreciable  delay  (i.e. 
that  of  sound)  to  a  lever  which  can  record  them  on 
a  revolving  cylinder  which  has  been  covered  with 
paper.  Now,  the  record  can  be  written  in  two  ways : 
either  according  to  the  Morse  Code,  by  making  or 
breaking  the  contact  between  the  pen  and  the  surface 
of  the  cylinder,  or  else  in  the  form  of  a  continuous 
curve,  the  variations  of  which  express  the  different 
phases  of  the  movement.* 

Chronographic  Record  of  the  Foot  in  Walking,  as  it 
touches  and  leaves  the  Ground. — A  cylinder  which 
turns  at  a  uniform  rate  is  covered  with  a  sheet  of 
paper,  while  the  points  of  two  tracing  needles,  which 
are   placed    side   by  side,  touch   the   surface   of    the 

I  cylinder,  one  of  them 

|  at   the   moment   the 

a  r  right    foot,   and    the 

%*.  \\      °tner  at  the  moment 

i.    ■  -    ..^■a^drel^^  V\      tlif   left   foot   readies 

m  ^^^^^^^^WJ     the  ground.    The  ob- 

^1 -^-^-s-^...  :.  "?^j^^      ment    is    that    each 

Fig.  3— Shoe  for  indicating   when   a  man's  foot  needle    shall  COme    in 

conies  in  contact  with  the  ground;  a  transmit-                               .    .  . 

ting  tube  effects  a  communication  between  the  COlltact  With  the  SUr- 

air  chamber  and  the  chroiiographic  tambour.  -  „      , 

face  ot  the  paper  as 
the  corresponding  foot  touches  the  ground.  The  trans- 
mission is  effected  by  means  of  pneumatic  tubes. 

A  particular  kind  of  shoe  (Fig.  3)  is  fitted  to  the  foot 
of  the  pedestrian,  and  the  sole  is  composed  of  a  thick 

*  For  the  different  applications  of  this  sort  of  written  record  see 
"  The  Graphic  Method,"  p.  426. 


TIME 


sheet  of  indiarubber,  provided  with  a  hollow  chamber. 
This  latter  cavity  communicates  through  a  long 
flexible  tube  with  the  recording  tambour.  Each  time 
the  foot  touches  the  ground  the  air  within  the  cavity 
of  the  sole  is  compressed,  and  passing  along  the  con- 
necting tube  raises  the  corresponding  recording  needle. 
The  pedestrian  furnished  with  a  pair  of  these  shoes 
(Fig.  4),  carries  in  his 
right  hand  the  record- 
ing apparatus  with  its 
registering  needles. 
When  he  wishes  the 
tracing  to  commence 
he  squeezes  an  india- 
rubber  ball  which  he 
holds  in  his  left  hand  ; 
if,  a  moment  later,  he 
releases  the  pressure, 
the  needles  cease  trac- 
ing. Records  are  thus 
obtained  which  vary 
according  to  the  pace, 
the  weight  carried,  and 
the  incline. 

Changes  in  the  se- 
quence and  duration  of 
the  footfalls  are  shown 
by  the  four  figures  in 
the  diagram  (Fig.  5).  In  this  the  contact  of  the 
right  foot  is  represented  by  a  white,  and  that  of  the 
left  by  a  diagonally  shaded  line.  The  first  of 
the  series  represents  walking  on  level  ground.  The 
steps  of  the  two  feet  are  alternate  and  regular. 
The  second  tracing  is  obtained  by  walking  upstairs; 
in  this,  one  foot  does  not  leave  the  ground  until  the 
other  one  has  been  down  some  time.     This  represents 


Fig  4. — Pedestrian  furnished  with  special  shoe?, 
and  carrying  a  chronographic  apparatus. 


8 


MOVEMENT 


one  of  the  phases  of  reduplicated  footsteps.  The 
third  is  that  of  a  runner.  The  periods  of  contact 
are  short,  and  separated  from  one  another  by  intervals 


Fig.  5. — Chronographic  record  of  the  periods  of  contact  of  the  feet  of  a  man  executing 
various  paces. 


during  which  neither  foot  is  in  contact  with  the  ground 
— a  period  of  suspension.  The  fourth  tracing  is  one 
of  a  man  running  at  a  greater  speed,  the  periods  of 
contact  are  shorter  and  the  intervals  longer. 

Record  of  the  Rise  and  Fall  of  the  Four  Feet  of  a 
Horse  in  its  Various  Pace?. — For 
some  time  past  specialists  gifted 
with  immense  powers  of  observa- 
tion have  set  themselves  the  task 
of  determining  the  real  character 
of  the  various  paces  of  a  horse 
from  observations  on  the  se- 
quence of  the  heat  of  the  feet. 
The  use  of  the  word  heat  im- 
plies an  attempt  to  recognize 
from  the  sound  of  the  footfalls 
the  sequence  of  the  moment  of 
contact,  the  question  of  dura- 
tion being  neglected.  Moreover, 
the  sense  of  hearing  is  above 
all  others  capable  of  appreci- 
ating  intervals  of   time.     The  effect    has    been   tried 


Fig.  6.  —  Special  apparatus  for 
recording  the  contacts  of  a 
horse's  fe<  t  with  the  ground; 
a  transmitting  tube  effects  a 
commun  cation  between  the 
air  chamber  and  the  chrono- 
graphic tambjur. 


TIME 


9 


of  providing  horses'  legs  with  bells  which  emit 
different  notes  as  each  foot  touches  the  ground.  All 
of  these  experiments  have  left  doubts  as  to  the 
exact  rhythm  of  the  various  paces,  doubts  which 
have  only  been  cleared  up  by  the  application  of 
chronograph}7.  The  following  method  has  been  em- 
ployed in  this  research  :  indiarubber  balls  stuffed  with 
hair  are  fixed  under  the  hoofs  of  the  horse,  and  kept 


Jig.  7.— Horse  at  a  full  trot.     The  point  indicated  on  the  chart  corresponds  to  the 
position  of  the  horse  represented  in  the  figure. 

in  position  by  calkins  which  screw  into  the  metal  of 
the  shoe.  Each  of  these  balls  is  in  connection  with  a 
long  indiarubber  tube  which  is  fastened  to  the  horse's 
legs  by  flannel  binders.  These  tubes  communicate 
with  the  recording  apparatus.  The  latter  is  provided 
with  a  tracing  needle,  and  held  in  the  hand  of  the 
rider   (Fig.  7).     The   pressure  of  the  feet  upon    the 


10  MOVEMENT 

ground  compresses  the  balls  with  which  they  are  pro- 
vided, and  forces  the  contained  air  into  the  recording 
tambours.  The  method  tallies  in  all  respects  with 
that  employed  in  the  case  of  man.  However,  on 
account  of  the  multiplication  of  writing  needles,  which 
the  greater  number  of  footfalls  necessitates,  the  four 
needles  are  grouped  in  two  series,  one  to  record  the 
movements  of  the  fore  feet,  and  the  other  placed 
beneath  it  to  record  the  steps  of  the  hind  feet.  In 
both  series,  the  white  lines  indicate  the  movements  of 
the  right  feet,  while  diagonally  shaded  ones  represent 
those  of  the  left. 

Fig.  8  shows  results  obtained  in  this  way  of  the 
three  ordinary  paces,  namely,  ambling,  walking,  and 
trotting.*  It  will  be  noticed  that  each  record  is  repre- 
sented as  a  series  of  four  tracings,  such  as  would  be 
obtained  by  arranging  in  parallel  series  the  tracings 
of  two  men  walking.  In  fact,  a  quadruped  may  be 
compared  to  two  bipeds — to  two  men,  for  instance — 
walking  one  behind  the  other,  one  to  represent  the 
fore,  and  the  other  the  hind  limbs.  Such  a  pair 
would  take  the  same  number  of  steps ;  but  the  phases 
of  rest  and  motion  would  assume  different  relations 
in  the  two  cases.  'It  is  this  which  constitutes  the 
difference  between  the  various  kinds  of  paces.  For 
instance,  when  the  corresponding  hind  and  fore  feet 
move  simultaneously,  the  horse  is  ambling  (Tig.  8,  first 
record).  If  the  right  fore  foot  is  in  the  mid  phase 
of  rest  when  the  left  hind  foot  reaches  the  ground, 
the  horse  is  walking  (second  record).  Lastly,  if  the 
anterior  and  posterior  legs  move  in  opposite  pairs, 
i.e.  if  the  anterior  right  reaches  the  ground  at  the 

*  It  is  more  than  twenty-one  years  ago  that  these  experiments  were 
made,  and  we  remember  with  gratitude  the  patient  assistance  with 
which  Messrs  P..  llier  and  Gabriel  Pail  lard  helped  us  to  carry  them 
into  effect. 


TIME  1 1 

same  time  as  the  posterior  left  leg,  the  horse  is 
trotting  (third  record).  It  is  thus  seen  with  what 
simplicity  the  ordinary  paces  of  a  horse  may  be 
recorded  both  as  regard  sequence  and  duration.*  Paces 
that  involve  a  springing  movement,  i.e.  the  various 
forms  of  galloping,  can  be  analyzed  with  equal  facility 
in  spite  of  their  greater  complexity. 


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Fig.  8.— Three  records  of  the  paces  of  a  horse :  amble,  walk,  and  trot. 

Fig.  9  is  the  record  of  the  ordinary  triple-heat 
gallop,  i.e.  that  in  which  the  combined  fall  of  the 
hoofs  produces  three  sounds  appreciable  to  the  ear. 
The  diagram  shows  how  the  three  sounds  are  produced. 

The  simple  interpretation  of  this  written  record  is 
that,  in  A,  the  first  sound  is  made  by  the  left  hind 
foot.  The  second  by  the  simultaneous  fall  of  the  left 
fore,  and  of  the  right  hind  foot.  The  record  demon- 
strates still  another  fact,  for,  in  B,  it  can  be  seen  by 
what  feet  the  body  is  at  any  moment  supported.  It 
is  clear  that  at  first  the  weight  falls  only  on  one  leg, 
then  on  three,  and  then  successively  on  two,  three, 

*  In  this  record  we  have  represented  the  trot  as  a  walking  pace, 
this  is  an  exceptional  ctse.  The  ordinary  trot  is  a  form  of  running, 
and  its  graphic  record  shows  a  moment  of  '"suspension,"  as  in  the 
case  of  a  man  running. 


12  MOVEMENT 

and  one.  In  the  final  stage,  the  horse  is  momentarily 
poised  in  the  air  before  it  again  comes  down  on  the 
left  hind  foot. 

The  Record  of  the  Fingering  of  a  Pianist. —  The 
facility  with  which  chronography  can  be  applied  to 
the  most  complicated  movements  of  irregular  sequence 
and  duration  has  encouraged  an  attempt  to  record 
movements  so  complex  as  to  defy  the  observation  of 
the  most  practised,  namely,  the  movements  of  the 
fingers  of  a  pianist  on  the  keyboard  of  his  instrument. 

Under  each  note  on  the  keyboard  of  a  harmonium 
is  placed  a  tiny  pair  of  bellows,  and  each  of  the  latter 
is  in  communication  by  means  of  a  special  tube  with 


3TEMP' 

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^^^^^ 

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Fir,.  9.—  Triple-beat  gallop.  A  indicates  the  exact  position  of  the  three  beats. 
B  indicates  the  number  of  feet  by  u  Licit  the  hoise  is  supported  at  any  particular 
moment  during  a  triple-beat  gallop. 

a  corresponding    pair,   which    in    turn   are  connected 

with  a  tracing  needle.    The  series  of  needles  are  placed 

in  a  row,  and  are  arranged  in  the  order  in  which  the 

different  notes  succeed  one  another  in  ordinary  music, 

namely,  in  an  ascending  scale  of  musical  pitch.     All 

these  needles  trace  their  record  on  a  strip  of  smoked 

paper  which  is  moved  by  clockwork.     Finally,  a  comb 

with  five  teeth  inscribes  the  stave  on  which  the  various 

notes  are  written  and  recognized  by  their  respective 

positions  in  relation  to  it.     The  duration  of  the  sound 

is* expressed  by  the  length  of  the  stroke.     Semitones 

are  distinguished  by  two  tiny  parallel  strokes,  instead 

of  a  single  broad  one.* 

*  This  method  of  notation  has  been  made  use  of  by  M.  V.  Tatin  in 
a  very  able  maimer. 


TIME 


13 


At  one  of  the  scientific  soirees  at  the  Sorbonne, 
during  a  conference  on  animal  movement,*  one  of  our 
associates,  a  celebrated  organist,  kindly  played  some 
pieces  of  music  which  recorded  themselves  before  the 
eyes  of  the  audience,  and  of  which  we  here  give  two 
examples    (Fig.   10,   A   and  B).      Every  one  who   is 


Fig.  10.— Record  of  two  airs  played  on  the  keyboard  of  a  harmonium. 

accustomed  to  read  ordinary  music  will  easily  decipher 
these  examples;  they  only  differ  from  the  ordinary 
score  by  the  way  in  which  the  duration  of  the  note 
is  expressed.  Instead  of  the  conventional  method  of 
expressing  the  duration  of  different  sounds  by  minims, 
crotchets,  and  quavers,  and  the  duration  of  silence 
by  rests  and  crotchet-rests,  the  graphic  method  conveys 
*  See  La  Nature,  5th  October,  1878. 
3 


14  MOVEMENT 

the  same  impression  by  the  length  of  the  stroke,  that 
is  to  say,  by  a  natural  graphic  expression.* 

The  Uses  of  Photography  in  recording  Time. — If  the 
recording  needle  cannot  be  applied  to  the  study  of 
any  particular  phenomenon,  recourse  must  be  had 
to  photography.  It  is  by  this  means  that  a  system 
of  optical  telegraphy  has  been  perfected,  by  which 
flashes  of  light  can  be  transmitted  from  one  point 
to  another,  and  received  as  a  series  of  dots  and  dashes, 
such  as  constitute  the  Morse  Code. 

The  luminous  point  at  the  transmitting  station  is 
alternately,  and  at  various  intervals,  exhibited  and 
obscured  by  the  movement  of  a  screen.  This  con- 
stitutes the  transmitting  apparatus.  The  rays  of  light 
emanating  from  this  source  are  rendered  parallel  by 
the  interposition  of  a  lens,  and  traverse  the  inter- 
vening space  to  impinge  upon  a  similar  lens  at  the 
receiving  station. 

At  the  focal  point  of  this  second  lens  the  image 
of  the  luminous  source  is  visible  in  the  form  of  a 
brilliant  spot.  If  the  sensitive  surface,  upon  which 
this  image  falls,  is  allowed  to  travel  at  a  uniform 
rate,  short  flashes  of  light  will  produce  spots,  and 
sustained  flashes  will  give  lines.  An  arrangement 
of  this  kind  has  many  scientific  applications,  but  it 
is  not  in  this  manner  that  photography  has  been 
most  usefully  employed  in  time-measurements.  It  has 
chiefly  been   utilized  for   two   purposes.      Firstly,  to 

*  During  late  years  many  inventors  have  constructed  similar 
machines,  and  we  believe  that  even  this  is  not  the  lirrt  which  auto- 
matically inscribed  an  air  executed  on  the  piano.  Among  instru- 
ments of  lecent  design  there  is  a  very  remarkable  one,  which  we 
owe  to  Messrs.  Cros  and  Carpentier,  and  which  is  known  as  the 
"Melograph."  This  instrument  is  not  intended  to  register  the  air 
as  played  by  the  artist,  but  it  perforates  a  strip  of  paper  in  such  a 
way  that  when  it  is  repassed  through  the  machine  the  piece  of  musio 
winch  has  b  en  executed  by  the  operator  is  reproduced  by  it  with 
perfect  fidelity. 


TIME  15 

measure  the  exposure  of  a  photographic  shutter ;  and 
secondly,  to  measure  the  intervals  of  time  which 
separate  consecutive  exposures.  Both  of  these  methods 
must  be  described,  since  it  is  necessary  to  be  familiar 
with  them,  so  as  to  understand  the  analysis  of  move- 
ment by  means  of  photography. 

Measurement  of  the  D  oration  of  Exposure  produced  by 
a  Photographic  Shutter. — Shutters  are  generally  called 
instantaneous,  when  they  show  in  the  photograph  a 
representation  of  a  moving  object  as  clearly  as  would 
have  been  the  case  had  the  object  been  at  rest.  This 
definition  is  not,  however,  strictly  true,  since  shutters, 
capable  of  giving  a  clear  picture  of  passengers  in  the 
street,  may  be  incapable  of  doing  so  in  the  case  of 
the  hoofs  of  a  trotting  horse.  A  still  shorter  time  is 
required  to  catch  the  various  positions  of  the  wing  of 
a  flying  bird,  and  still  more  so  in  the  case  of  insects. 
It  must  be  possible  then  to 
measure  the  exposure  of  a 
shutter,  and  express  the  time 
in  fractions  of  a  second. 

We  shall  see  how  photo- 
graphy allows  this  measure- 
ment to  be  made.  Let  a 
bright  needle  rotate  on  a  dial 
(Fig.  11)  covered  with  black 
velvet,  and  graduated  by  white  f.-..  n.-Needie  spinning  round  the 

!•  mi  .        n.     .i  chr.  nomotr  c  dial,  and  measurin-' 

lines.       lhe    movement    01     the        the  duration  of  exposure. 

needle     must     be     absolutely 

uniform.  For.  this  purpose  clockwork  machinery 
with  a  Foucault's  regulator  is  employed.  This 
mechanism  is  hidden  behind  the  dial,  and  the  needle 
makes  one  complete  revolution  in  a  second  and  a  half, 
say  90'".  The  circumference  of  the  dial  is  divided 
into  eighteen  equal  parts,  and  consequently  the  con- 
tained angle  of  each  space  corresponds  to  5"\ 


16  MOVEMENT 

While  the  needle  is  constantly  rotating,  we  must 
focus  on  the  dial  a  camera  provided  with  the  shutter, 
the  exposure  of  which  we  wish  to  ascertain.  The 
opening  of  the  shutter  is  effected  by  pressure  on  an 
indiarubber  ball.  If  the  period  of  exposure  is  not 
extremely  short,  the  image  of  the  needle  will  not  be 
clearly  defined,  but  will  occupy  a  more  or  less  ex- 
tensive segment  of  the  dial.  In  such  cases  it  would 
be  impossible  to  determine  with  any  exactitude  the 
number  of  degrees  occupied  by  the  image.  This  is 
due  to  the  construction  of  the  shutters,  which  give 
incomplete  illumination  at  the  beginning  and  end 
of  the  exposure.* 

From  the  blurred  nature  of  the  image,  which 
obscures  the  exact  contour  of  the  needle,  one  can  only 
approximately  estimate  that  the  distance  travelled 
during  a  single  exposure  is  about  three  or  four 
degrees,  which  corresponds  to  about  £$  of  a  second. 

It  is  almost  impossible  for  a  shutter,  which  gives  a 
single  exposure,  to  produce  one  of  very  short  duration. 
For  this  object,  the  spring  which  moves  the  shutter 
must  be  very  powerful,  and  the  weight  carried  ex- 
tremely light.  With  shutters  of  this  kind  it  is  possible 
to  reduce  the  exposure  to  2^0  of  a  second. 

The  shutters  referred  to  in  this  work  are  of  special 
construction.  They  consist  of  fenestrated  diaphragms 
which,  by  means  of  continuous  rotation,  are  able  to 
acquire  immense  velocity.  Their  fenestrations,  moving 
within  the  lens  with  extreme  rapidity,  produce  a 
succession  of  illuminations  of  very  short  duration. 

It  is  this  which  gives  such  good  definition  to  the 
images,   which  are  shown  in  Fig.   12.     Further,  the 

*  To  obtain  a  true  idea  of  the  outline  of  the  needle,  it  should 
be  r-ompared  with  the  image  of  big.  12.  In  tin's  ease  the  exposure 
has  been  short  enough  to  prevent  any  alteration  in  its  shape  through 
the  movement. 


TIME 


17 


images  succeed  one  another  at  absolutely  regular 
intervals,  because  both  the  movement  of  the  needle 
on  the  dial  and  that  of  the  circular  diaphragms  are 
equally  uniform. 

Measurement  of  the  Intervals  of  Time  which  separate 
Successive  Exposures. — By  reason  of  the  clear  definition 
of  the  images,  they  can  be  accurately  measured,  not 
by  the  time  of  exposure,  which  is  too  short  to  be 
appreciated,  but  by  the  in- 
tervals of  time  between  suc- 
cessive exposures.  Now,  this 
is  the  important  point  in  the 
measurements  which  we  shall 
have  to  make  of  the  duration 
of  certain  phenomena. 

Provided  that  one  can  ar- 
range a  reliable  clockwork 
mechanism  so  as  to  move  the 
needle  round  the  dial  at  a 
uniform  rate,  it  does  not  mat- 
ter  what    rate    of  movement 

is  imparted  to  the  circular  diaphragms,  the  interval 
between  two  exposures  can  always  be  measured  by 
the  angle  contained  between  two  consecutive  images 
of  the  needle.  If,  during  the  time,  an  object,  visible 
in  the  field  of  the  lens,  happens  to  move,  there  will 
be  found,  on  the  sensitized  plate,  several  of  its  images 
in  various  positions  and  at  various  distances  from  one 
another.  For  the  purpose  of  measuring  the  intervals 
of  time  between  such  successive  positions  of  the  object, 
the  changes  in  position  of  the  needle  on  the  chrono- 
graphic  dial  will  serve  as  an  index. 

The  further  applications  of  this  kind  of  time 
measurement  will  be  seen  when  we  come  to  discuss 
Chronophotography. 


Fig.  12.— Successive  positions  of 
the  needle  on  the  chronomeiric 
dial,  measuring  the  intervals  of 
time  separating  the  successive 
exposures. 


CHAPTER  II 

SPACE 

Its  Measurement  and  Representation  by 
Photography 

Summary. — Tendency  to  replace  outline  drawings,  plans,  and  diagrams 
in  relief  by  photography — Photography  traces  the  various  positions 
in  space  occupied  by  a  moving  body  — Photographic  trajectory 
of  the  movements  of  a  point  in  space ;  its  stereoscopic  trajectory 
— Movements  of  a  straight  line  in  space — Solid  figures  formed 
thereby :  cylinders,  hyperboloids,  cones,  etc. — Movements  of  a 
curve  in  space ;  photography  <  f  the  figures  which  it  forms : 
spheres,  ellipsoids,  etc.  — Stereoscopic  pictures  of  figures  of  three 
dimensions — Figures  formed  by  the  movement  of  solid  bodies; 
effects  of  light  and  shade. 

Tendency  to  replace  Outline  Drawings,  Plans,  and 
Diagrams  in  Relief  by  Photography . —The  positions  of 
bodies  in  space,  their  forms  and  dimensions,  find 
their  natural  expression  in  geometrical  drawings.  Such 
drawings,  executed  to  a  known  scale,  supply  all  the 
information  that  is  required. 

During  the  last  few  years,  however,  there  has  been 
a  tendency  to  substitute  photography  for  outline 
drawings,  and  doubtless  in  the  future  it  will  completely 
replace  them.  Indeed,  it  supplies  with  remarkable 
ease  pictures  of  undoubted  accuracy.  The  dimensions 
can  be  enlarged  or  reduced  as  occasion  may  require., 
and  if  thought  desirable,  a  scale  for  the  purpose  of 
measurement  may  be  introduced,  into  the  picture,  and 


SPACE  19 

the  exact  dimensions  thus  indicated.  To  introduce 
such  a  scale,  into  the  picture,  a  rule  with  very  distinct 
divisions  must  be  placed  by  the  side  of  the  object 
which  is  being  photographed.  When  an  artist  wishes 
to  represent  in  relief  an  object  of  three  dimensions, 
he  must  obey  the  laws  of  perspective,  and  take  into 
consideration  the  manner  in  which  the  light  falls  on 
the  object,  at  the  moment  of  drawing.  But  the  fitful 
changes  of  light,  during  the  various  times  of  day,  offer 
innumerable  difficulties. 

Photography,  however,  gives  an  instantaneous  picture 
of  the  most  diverse  objects,  and  that,  too,  with  the 
prevailing  conditions  of  light,  and  all  in  correct 
perspective.  The  appearance  of  natural  objects,  as 
seen  by  looking  with  one  eye  only,  is  thus  repro- 
duced by  photography.  If  it  is  required  to  get 
the  effect  of  relief,  such  as  is  obtained  bv  looking 
with  both  eyes,  recourse  must  be  had  to  stereoscopic 
pictures. 

Photography  traces  ths  Various  Positions  in  Space 
occupied  by  a  Moving  Body. — When  an  object  changes 
its  position,  it  is  often  necessary  to  notify  the  posi- 
tions in  space  which  it  successively  occupies.  In  the 
first  place,  we  must  be  quite  sure  that  our  eyes  have 
boen  able  to  follow  the  various  phases  of  movement, 
and  that  our  memory  has  been  able  to  retain  the 
details— conditions  rarely  fulfilled — before  we  have 
recourse  to  drawing,  as  a  means  of  representing  the 
trajectory  described.  The  diagram  traced  will  be 
more  or  less  complicated  according  as  we  express  the 
movement  by  a  point,  a  line,  a  plane  superficies,  or  a 
solid — in  short,  according  as  we  represent  a  movement 
executed  in  one  or  more  directions. 

When  it  is  only  a  question  of  the  movement  of  a 
point,  in  certain  cases  the  difficulty  may  be  met  by 
making  the  moving  point  itself  trace  the  path  which 


20  MOVEMENT 

it  takes.*  It  must  be  possible,  however,  to  fasten  this 
point  directly  or  indirectly  to  the  needle  which  is  to 
trace  the  trajectory,  and,  further,  the  propelling  force 
must  be  sufficient  to  work  the  mechanism  of  the 
recording  instrument,  and  that,  too,  without  modifica- 
tion of  the  movement.  But  if  the  point  is  inaccessible, 
if  the  propelling  force  is  too  feeble,  or  if  it  follows 
a  very  complicated  course,  we  must  introduce  new 
conditions,  and  employ  photography  in  the  special 
manner  we  are  about  to  describe. 

Principles  of  Photography  with  a  Dark  Background. — 
When  a  camera  faces  a  dark  background,  no  impression 
is  made  on  the  sensitized  plate,  because  no  light 
reaches  it;  but  if  a  very  luminous  object  is  placed 
between  the  background  and  the  lens,  light  will  be 
reflected  and  an  image  imprinted  on  the  plate.  If, 
while  the  object-glass  is  uncovered,  the  white  object 
changes  its  position,  there  will  be  reproduced  on  the 
plate  a  track  which  exactly  corresponds  to  the  move- 
ments of  the  object.  This, is  the  trajectory  of  the 
object,  or,  to  put  it  more  precisely,  the  projection  of 
its  trajectory  on  the  surface  of  the  sensitized  plate. 
The  image  will  be  more  or  less  reduced  in  size 
according  to  the  distance  of  the  object,  and  according 
to  the  focal  length  of  the  objective. 

Photographic  Trajectory  of  the  Movements  of  a  Point 
in  Space. — To  demonstrate  the  advantages  offered  by 
photography  as  a  means  of  recording  the  trajectory  of 
a  moving  object,  we  will  choose  as  an  example  a  case 
in  which  direct  observation  will  afford  us  no  informa- 
tion, and  in  which  a  mechanical  method  of  recording 
will  be  impracticable.  Suppose,  for  example,  that 
we  wish  to  ascertain  the  various   positions  in   space 

*  The  different  proceedings  for  mechanically  recording  the  move- 
ments of  a  point  in  one  or  more  directions  in  space  have  been  given  in 
"  The  Graphic  Method." 


SPACE  2 I 

occupied  by  a  particular  part  of  a  bird's  wing  during 
the  act  of  flight,  and  that  this  particular  part  is  the 
tip  of  one  of  the  quills,  called  "remiges."  Now,  such 
a  quill,  by  reason  of  its  flexibility,  would  be  incapable 
of  giving  the  necessary  motive  power  to  an  apparatus 
for  recording  the  trajectory  of  flight ;  and,  further,  this 
point  is  inaccessible  because  birds  only  fly  freely  at 
a  certain  distance  from  the  observer.  A  black  crow 
may  be  used  in  the  experiment,  and  a  small  piece  of 
white  paper  may  be  fixed  to  the  extremity  of  one  of  its 


Fig.  13. — Trajectory  of  the  tip  of  a  crow's  wins.  A  brilliant  spangle  attached  to  the 
second  of  the  remiges  follows  the  path  indicated  by  tie  small  arrows.  In  the  lower 
part  of  the  figure  a  straight  and  horizontal  arrow  sho»\s  the  direction  of  flight. 

longest  "remiges."  The  bird  is  then  allowed  to  fly 
in  front  of  a  dark  background,  towards  which  a  photo- 
graphic camera  is  directed.  Since  the  entire  field  of 
the  object-glass  is  dark,  that  is  to  say,  the  bird  and  its 
background,  the  sensitized  plate  can  receive  no  light 
except  that  which  is  reflected  by  the  small  piece  of 
white,  paper,  which  is  illuminated  by  the  sun.  The 
image  of  this  white  spot  will  leave  a  record  of  its 
track  on  the  sensitized  plate.  In  this  way  Fig.  13  was 
obtained,  the  arrows  indicating  the  direction  of  flight. 
Stereoscopic    Trajectories. — The    trajectory    of    the 


22  MOVEMENT 

movement  of  the  point  of  a  wing  cannot  be  expressed 
comprehensively  in  the  form  of  a  plane  diagram,  since 
the  movement  of  the  wing  at  the  shoulder-joint  takes 
place  in  three  directions.  The  photographic  diagram 
only  gives  one  projection  of  this  trajectory.  It  is  thus 
incapable  of  expressing  the  real  course  of  flight  taken. 
If  a  movement  takes  place  in  three  directions,  recourse 
must  be  had  to  a  more  complicated  arrangement,  and 
a  stereoscopic  trajectory  obtained.  Let  us  take  the  case 
of  a  man  walking  away  from  us,  and  concentrate  our 
attention  on  a  particular  point  of  his  body.  This  point 
is  elevated  and  depressed  as  the  man's  foot  rises  and 
falls.  Further,  it  is  affected  by  the  side-to-side  swing, 
and  according  to  the  direction  in  which  he  walks. 
The  pedestrian  must  be  completely  dressed  in  black, 
and  a  bright  metal  button  fastened  to  a  part  of  his 
body.  The  man  is  then  made  to  walk  in  front  of  a 
dark  background,  and  a  stereoscopic  photographic 
camera  with  two  lenses  is  focussed  on  the  spot.  Both 
of  these  object-glasses,  acting  precisely  as  the  single 
one  in  the  preceding  experiment,  produce  two  images 
of  the  luminous  point. 

Fig.  14  was  obtained  in  this  manner ;  it  shows  two 
images  of  the  same  trajectory  taken  from  two  different 
points  of  view.  Examined  with  the  stereoscope,  these 
images  stand  out  in  bold  relief.* 

*  Since  a  considerable  number  of  people  are  able  to  see  figures  of 
this  sort  standing  out  in  relief  without  having  recourse  to  a  stereo- 
scope, we  have  published  the  above  figure,  find  certain  others  will 
be  found  further  on.  To  obtain  the  full  effect  of  relief  without  :i 
stereoscope,  we  must  concentrate  our  vision  on  a  distant  point,  and 
then  interpose  the  object  between  our  eyes  and  the  distant  point.  The 
page  of  the  book  will  then  be  seen  double,  and  consequently  the  tra- 
jectory will  upper  as  four  separate  images.  If  the  book  is  then  very 
gently  moved,  and  the  direction  of  the  eyes  slightly  alten  d,  the  two 
internal  images  finally  become  exactly  superimposed.  The  eye  is 
then  accommodated  for  distinct  vision  of  the  central  image,  which 
stands  out  in  relief  between  the  two  outlying  images. 

With  a  little  practice  one  can  easily  dispense  with  the  stereoscope 
for  examining  figures  of  this  sort, 


SPACE  23 

Movements  of  a  Straight  Line  in  Space.  Photography 
of  the  Solid  Figures  formed  thereby :  Cylinders,  Hyper- 
boloids,  Cones,  etc.  — A  straight  line,  which  is  moved 
in  various  ways  on  a  plane  surface,  covers  the  latter 
with  a  variety  of  configurations,  or  else,  if  attention 
is  paid  only  to  the  various  positions  which  it  occupies 
at  certain  moments,  these  positions  can  be  expressed 


Fig.  14.— Stereoscopic  trajectory  of  a  brilliant  point  pliced  at  the  level  of  ihe  lumbar 
vertebra;  of  a  man  walking  a\\\iy  from  tue  photographic  camera. 

as  geometrical  figures,  which  can  be  transferred  to 
paper ;  but  if  this  straight  line  moves  in  the  three 
directions  of  space  it  describes  surfaces,  the  projec- 
tions of  which  can  only  be  represented  by  perspective 
drawing.  In  such  cases  recourse  must  be  had  to 
diagrams  in  relief,  which  have  the  advantage  of  giving 
beginners  a  clearer  notion  of  solid  forms.  By  means 
of  threads  stretched  between  metal  armatures,  one  can 


24  MOVEMENT 

show  how  the  successive  positions  of  a  straight  line 
can  produce  cylinders,  cones,  conoids,  and  hyperboloids 
by  revolution.  There  is  a  particularly  rich  collection 
of  such  diagrams  at  the  Academy  of  Arts  and  Crafts 
— very  useful  as  a  means  of  popularizing  the  study 
of  solid  geometry. 

Now,  if  the  geometry  of  to-day  has  become  purely 
a  speculative  science,  there  is  no  doubt  that,  like  all 
other  sciences,  it  had  an  experimental  origin.  It  is 
not  likely  that  the  conception  of  a  straight  line  was 
evolved  from  man's  brain  as  a  purely  abstract  ex- 
pression, but  rather  that  it  entered  therein,  on  seeing 
a  stretched  thread,  for  instance,  or  some  other  recti- 
linear object. 

In  the  same  way  the  conception  of  a  plane  or  a 
circle  found  its  origin  from  noticing  a  flat  surface  or 
an  object  of  circular  form. 

There  are,  so  to  speak,  traces  of  these  concrete 
origins  of  geometrical  figures  in  the  definitions  given 
to  solid  figures  or  to  those  of  three  dimensions. 

Such  objects  are  said  to  be  "  engendered  "  by  straight 
lines  or  curves,  which  undergo  various  displacements. 
Thus  a  regular  cylindrical  surface  is  engendered  by 
a  straight  line  which  moves  parallel  to  another,  straight 
line,  and  yet  remains  at  the  same  distance  from  it. 
The  straight  line  which  moves  is  the  "  generator  "  of 
the  cylinder ;  that  which  remains  fixed  is  its  axis. 

Under  such  circumstances,  let  us  suppose  that  the 
straight  line,  as  it  moves  in  space,  leaves  a  record  of 
its  track  at  every  point  which  it  successively  passes. 
Now,  this  purely  imaginary  supposition  may  become 
an  accomplished  fact,  thanks  to  photography.  Indeed, 
supposing  we  take  a  series  of  instantaneous  views  of 
an  illuminated  thread  as  it  moves  in  front  of  a  dark 
screen,  figures  are  produced  which  exactly  resemble 
the  stereoscopic  forms  obtained  by  stretching  a  series 


srACE  25 

of  threads  between  metal  armatures,  This  is  the 
method  : — 

A  vertical  metal  rod  furnished  with  two  transverse 
arms,  Avhieh  are  exactly  opposite  to  one  another,  is 
allowed  to  rotate  in  front  of  a  dark  screen.  This 
metal  frame  must  be  blackened  with  the  smoke  of  a 
candle,  and  thus  rendered  as  nearly  invisible  as 
possible.  The  two  cross-bars  must  be  of  equal  length, 
and  their  free  extremities  connected  by  a  white  thread, 
which  is  stretched  vertically  between  them.  This 
thread,  by  means  of  the  rotatory  motion  which  is 
imparted  to  the  two  cross-bars,  moves  in  a  circular 
manner  round  the  axis,  and  describes  in  space  the 
circular  outline  of  a  cylinder. 

A  photographic  camera  directed  towards  this  thread, 
and  kept  permanently  open,  would  receive  an  image, 
which  would  be  the  projection  of  a  cylinder  on  a  plane 
surface.  But  this  continuous  trajectory  would  not 
show  its  method  of  production  with  sufficient  clear- 
ness. In  order  that  one  may  see  that  such  a  picture 
results  entirely  from  the  movement  of  the  thread, 
which  at  every  moment  adds  a  new  component- 
element  to  the  surface  of  the  cylinder,  separate  images, 
at  successive  intervals  of  time,  must  be  obtained. 
That  is  to  say,  the  light  must  be  admitted  in  an  inter- 
mittent manner.     Fig.  15  was  thus  obtained.* 

If  the  thread,  instead  of  lying  parallel  to  the  axis 
round  which  it  rotates,  is  directed  obliquely  towards 
it,  the  figure  described  will  be  a  hyperboloid  by 
revolution  (Fig.  16).     And,   finally,  if  the  thread  is 

*  In  this  diagram  the  central  axis  appe  <rs  white,  because,  although 
the  amount  of  light  reflected  from  such  a  blackened  surface  is  ex- 
tremely feeble,  nevertheless,  this  light  is  always  reflected  on  to  the 
plate  every  time  the  objective  is  uncovered. 

Now,  since  the  axis  remains  permanently  in  one  place,  each 
separate  impression,  however  feebl",  is  superimpos  d  on  the  same 
part  of  the  s^nsitizt  d  plate,  and  ends  by  being  clearly  defined. 


26 


MOVEMENT 


placed  still  more  obliquely— in  fact,  if  it  touches  the 
axis  at  one  point — the  figure  described  will  be  a 
cone. 

Photography,  with  a  dark  background,  is  especially 
adapted  for  demonstrating  the  construction  of  cones 
and  hyperboloids ;  and,  further,  it  clearly  shows  the 
relations  which  these  two  kinds  of  figures  bear  to 
one  another. 

An  indefinite  number  of  images  can  be  taken  on 


Fig.  15.— Cylinder  engendered  by  the 
displacement  of  a  white  thread  mov- 
ing round  a  central  axis. 


Fig.  16.  — Hyperboloid  by  revolution: 
a  s-ingle  web  engendered  by  the 
revolut'on  of  a  thread  stt  obliquely 
to  the  axis. 


the  same  plate.  No  sooner  has  one  image  been  taken 
than  another  can  be  superimposed ;  the  second  im- 
pression is  just  as  good  as  the  first.  This  method  was 
employed  in  the  production  of  Fig.  17.  After  having 
taken  a  photograph  of  a  hyperboloid  by  revolution, 
the  dark  slide  was  closed,  and  the  thread  arranged  so 
as  to  describe  a  cone ;  the  slide  was  then  opened  again, 
and  the  image  of  the  cone  obtained.    The  two  pictures 


SPACE 


27 


thus  superimposed  show  the  hyperboloid  on  the  out- 
side and  its  asymptotic  cone  inside. 

Conoids. — If  the  white  thread,  instead  of  revolv- 
ing round  the  axis, 
as  in  the  experiment 
which  we  have  just 
been  reading,  has  im- 
parted to  it  at  one 
extremity  a  rotatory 
motion,  while  the  other 
extremity  moves  in  a 
straight  line,  one  ob- 
tains, according  to  the 
relationship  of  the  two 


movements,  different 
sorts  of  conoids,  of 
which  Fig.   18  is. one 


Fig.  17. — Hyperboloid  by  revolution  with  its 
asymptotic  cone. 


example. 

Movements  of  a  Curve  in  Space.     Photography  of  the 
Figures  which  it  forms:  Spheres,  Ellipsoids,  etc. — Among 


F.g.  18.— Conoid  engendered  by  the  move- 
nient  of  a  white  thread. 


Fig.  19. — Sphere  engendered  by 
the  rotation  of  a  semi-annular 
white  thread. 


the  forms  arising  from  the  movements  of  a  curve,  the 
most  easy  to  produce  is  a  sphere  ;  it  is  obtained  when 


28  MOVEMENT 

a  semicircular  wire  of  white  metal  rotates  round  a 
vertical  axis,  which  is  also  its  diameter.  Fig.  19  is 
the  projection  of  such  a  sphere  on  a  plane  surface. 
(The  imperfections  of  the  figure  are  due  to  the  fact 
that  it  is  impossible  to  impart  perfect  regularity  of 
curvature  to  the  wire  which  constitutes  the  semicircle.) 
It   is   unnecessary    to   multiply    examples   of    figures 


Fi:.  20.— Sphere  engendered  bv  thn  rotation  of  a  semi-annular  tbrcai. 
(Steri-osco,  ic  images  ) 


Fig.  21. — Hyperboloid  and  its  asymptotic  cone.     (Stereoscopic  images.) 

generated  by  the  movement  of  curves,  such  as  ellip- 
soids, paraboloids  by  revolution,  etc. 

In  order  that  these  figures  of  three  dimensions  may 
be  rendered  more  intelligible,  we  have  reproduced 
them  in  the  form  of  stereoscopic  pictures  by  the 
following  proceeding. 

Stereoscopic  Pictures  of  Figures  of  Three  Dimensions. — 
We  must  provide  ourselves  with  a  stereoscopic  camera 


SPACE  29 

with  two  object-glasses  of  equal  foeal  lengths.  The 
mountings  of  these  objectives  must  be  cleft  by  a  deep 
slot,  perpendicular  to  their  axes ;  and  within  this  slot 
there  must  rotate  a  diaphragm  perforated  by  two 
openings,  which  are  diametrically  opposite  to  one 
another.  This  diaphragm  rotates  at  a  uniform  rate, 
and  simultaneously  uncovers  the  two  objectives;  during 
each  complete  revolution  of  the  diaphragm  the 
objectives  are  twice  uncovered.  A  mechanical  motor 
turns  the  circular  diaphragm,  and,  by  means  of  a  pulley 


Fig.  22.— Sphere  engendered  by  tie  rotation  of  a  semi-annular  band,  white  o".  the 
outer  surface  and  black  on  the  inner  s:de. 

and  continuous  band,  the  same  motor  serves  to  turn 
the  axis  and  the  white  threads.  The  latter,  by  their 
movements,  describe  the  desired  figures. 

Figures  formed  by  the  Movement  of  Solid  Bodies; 
Effects  of  Light  and  Shade. — Instead  of  the  fine  thread, 
which  has  just  served  our  purpose  for  describing  the 
surface  of  a  sphere  in  space,  let  us  take  a  solid  body ; 
the  appearance  of  the  figure  described  will  be  quite 
different.  A  band  of  Bristol  board  is  arched  length- 
wise, its  convex  surface  blackened,  and  its  concave 
4 


30  MOVEMENT 

surface  left  white ;  when  such  a  band  rotates,  a  figure 
such  as  Fig.  22  will  be  produced.  Except  for  certain 
breaches  of  continuity,  due  to  the  intermittent  character 
of  the  illumination,  the  surface  thus  produced  will 
resemble  that  of  a  solid  sphere,  which  is  illuminated 
from  the  left  and  from  above,  while  the  opposite  side 
is  only  feebly  lighted  by  reflection.  This  appearance 
is  easily  explained.  The  strip  of  paper,  as  it  travels 
over  successive  meridians  of  this  imaginary  circle,  is 
placed  under  exactly  the  same  conditions  of  illumina- 
tion as  would  be  the  case  if  the  meridians  were  those 
of  a  real  sphere  in  the  same  position. 

Paradoxical  Effect  produced  by  Certain  Conditions  of 
Illumination. — Instead  of  the  strip  of  paper  used  in  the 
preceding  experiment,  and  from  which  light  was  only 
reflected  from  the  convex  surface,  let  us  take  a  strip 
of  similar  board,  only  white  on  both  surfaces.  We  shall 
thus  obtain  a  peculiar  effect  (Fig.  23)  which  can  only  be 
understood  when  viewed  under  stereoscopic  conditions. 

The  inner  and  outer  surfaces  of  this  sphere  can  be 
seen  at  one  and  the  same  time.  This  is  because  the 
arc  of  Bristol  board  is  white  within  as  well  as  without, 
and  consequently  reflects  the  light,  sometimes  from 
one  surface,  sometimes  from  the  other,  according  to 
the  position  of  rotation.  When  the  convex  arc  faces 
the  light,  i.e.  is  directed  upwards  and  towards  the  left, 
the  corresponding  portion  of  the  engendered  sphere 
is  clearly  visible.  When  the  arc  is  in  an  exactly 
opposite  phase  of  rotation,  it  receives  the  light  on  its 
concave  aspect ;  that  is  to  say,  the  interior  of  the 
sphere  below  and  on  the  left  is  the  part  illuminated. 

At  first  sight  this  figure  appears  to  be  transparent, 
but  on  the  one  hand  we  know  that  it  has  been  formed 
by  an  opaque  substance,  and  on  the  other  that  all 
known  transparent  media  reflect  light  in  a  totally 
different  manner. 


SPACE 


31 


Tn  reality  we  are  dealing  with  a  hypothetical  figure, 
which  finds  no  counterpart  in  Nature.  Such  hypo- 
thetical figures  are  still  more  strange,  when,  instead 


of  dull  substances  being  employed  in  their  construc- 
tion, a  polished  material  is  made  use  of  which  only 
reflects  the  sun's  rays  from  certain  points  of  its  surface. 


32 


MOVEMENT 


Fig.  24. — Paradoxic*)  1  appearance  of  a 
sphere  engendered  by  tlie  rotation  of 
a  brilliant  metallic  thread. 


Fitr.  24  was  obtained  by  allowing  a  semicircular  arc  of 
polished  brass  to  rotate  round  a  vertical  axis.  There 
is  for  each  position  of  rotation  only   one   particular 

spot  on  the  polished 
metal  arc  from  which  the 
incidental  rays  of  the  sun 
can  be  reflected  into 
the  body  of  the  camera. 
Now,  as  this  bright  spot 
changes  its  position,  it 
is  sometimes  on  the  con- 
vex side  and  sometimes 
on  the  concave  side  of 
the  metal  arc.  It  is  the 
displacement  of  this  lumi- 
nous spot  which  traces  the 
complete  rings  on  the  opposite  portions  of  the  sphere. 
In  order  more  clearly  to  understand  the  causation  of  this 
peculiar  appearance,  we  must  have  recourse  to  stereo- 
scopic figures,  with  an  intermittent  series  of  images. 
Such  figures  show  that  in  each  position  certain  portions 
of  the  surface  of  the  semicircular  arc  are  dark,  that 
is  to  say,  do  not  transmit  light  in  the  direction  of  the 
photographic  apparatus;  on  the  contrary,  other  points 
are  brilliantly  illuminated,  because  in  this  position 
they  are  "  set,"  so  to  speak,  so  as  to  reflect  the  sun's 
rays.  These  curious  effects  can  never  be  caused  by  a 
real  body.  The  form  and  position  of  the  illuminated 
spots  on  the  sphere  can  be  varied  at  will  by  changing 
the  direction  of  incidence  of  the  luminous  rays. 

The  mathematical  study  of  these  diverse  effects 
would  be,  perhaps,  rather  complicated ;  in  any  case,  it 
would  afford  a  very  limited  amount  of  interest.  It 
was  necessary,  however,  to  mention  them,  because  in 
the  course  of  our  studies,  we  shall  meet  with  analogous 
forms,  produced  by  the  movement  of  certain  bodies. 


CHAPTER   III 

MOVEMENT 

Its  Measurement,  Graphic  Representation,  and 
Analysis  by  means  of  Chronophotography 

Summary. — The  understanding  of  a  movement  implies  a  double 
knowledge,  namely,  that  of  space  as  well  as  that  <  f  time — 
Graphic  representation  of  a  movement — Chart  of  a  tiain  travel- 
ling a  ong  a  line — The  curve  of  a  prolonged  movement  should 
hij  recorded  in  sections  — How  a  moving  body  can  record  its  own 
movement  —  Proportional  enlargement  and  reduction  of  the 
recorded  movement — Odography — Photographic  record  of  move- 
ment—Photography  of  the  movement  of  Lippmann's  electrometer 
— Determination  by  means  of  chronophotography  of  the  move- 
ments executed  by  a  fnllin^  body — Construction  of  the  curves 
of  movement  from  chronophotographic  images — Time-curve  of 
the  distance  traversed — Curve  of  velocity — Curve  of  acceleration. 

The  Understanding  of  a  Movement  implies  a  Double 
Knowledge,  namely,  that  of  Space  as  well  as  that  of 
Time. — We  saw  in  Chapter  II.  that  photography 
could  reproduce  the  trajectory  of  a  body  moving  in 
space ;  but  the  idea  there  conveyed  of  the  successive 
changes  in  position  was  not  sufficient  to  define  the 
movement.  The  power  to  do  so  presupposes  a  know- 
ledge of  the  relationship  existing  at  any  moment 
between  the  distance  traversed  and  the  time  occupied. 
Now,  the  object  of  Chapter  I.  was  to  demonstrate  that 
photography  would  permit  the  exact  measurement  of 
time  intervals.  It  follows  that,  if  the  two  notions 
of  time  and  space  can  be  combined  in  photographic 


34  MOVEMENT 

images,  we  have  instituted  a  chronophotographic 
method,  which  explains  all  the  factors  in  a  move- 
ment which  we  want  to  understand.  It  also  affords  a 
very  simple  experimental  solution  of  certain  very 
complicated  mechanical  problems.  The  whole  ques- 
tion of  mechanics  is  based  on  a  knowledge  of  the 
movement  which  is  imparted  to  a  mass ;  for  from 
the  movement  the  force  which  produces  it  can  be 
measured. 

To  determine  with  accuracy  the  character  of  a 
movement,  whether  it  be  uniform  or  irregular,  to 
determine  its  velocity  and  degree  of  acceleration 
extremely  delicate  experiments  are  usually  necessary. 

When  the  movement  is  once  thoroughly  under- 
stood, its  character  must  be  expressed  in  a  precise 
manner.  Since  the  time  of  Descartes,  geometricians 
have  known  how  to  express  the  characters  of  move- 
ments in  the  form  of  curves  with  different  variations. 
But  such  curves,  although  they  can  express  certain 
phenomena,  require,  like  other  geometrical  figures,  a 
more  or  less  laborious  construction.  It  was  a  great 
step  in  advance  when  Poncelet  and  Morin  showed 
that  a  moving  body  could  itself  be  made  to  trace  its 
path  in  the  form  of  a  curve.  The  first  application 
of  this  graphic  method  was  made  use  of  in  the  case 
of  a  falling  body  ;  it  was  soon,  however,  extended  to 
other  branches  of  Science.  Meteorology,  Physics, 
and  Physiology  all  participated  in  the  discovery  with 
advantage  to  themselves. 

In  spite  of  the  enormous  development  of  this  method, 
it  has  limitations,  which  we  can  only  extend  by  the 
employment  of  chronophotography.  Thus,  when  the 
moving  body  is  inaccessible,  when  it  cannot  be  fastened 
by  mechanical  means  to  the  recording  apparatus,  this 
new  method  for  determining  its  movement  must  be 
employed  ;  a  method  which  demands  no  material  link 


MOVEMENT 


35 


Time  in  minutes 
c     i"      2-     y     w     5' 


I, 


between  the  visible  point  and  the  sensitized  plate  on 
which  from  moment  to  moment  its  movement  is 
recorded.  To  fully  appreciate  the  advantages  of 
chronophotography,  it  will  doubtless  be  best  to 
compare  it  with  other  methods  already  employed  in 
the  solution  of  the  same  problems.  Let  us  take  the 
most  simple  case,  that  of  recording  the  displacement 
in  a  straight  line  of  a  moving  body,  and  let  us 
approach  the  question  in  accordance  with  the  two 
methods. 

Graphic  Representation  of  Movement. — When  a  point 
travels  along  a  straight  line,  the  successive  positions 
can  be  indicated  by  means  of  two  straight  lines  at 
right  angles  to  one  another. 
These  two  straight  lines,  the 
one  horizontal  and  the  other 
vertical,  indicate  respectively 
the  time  taken  and  the  dis- 
tance traversed.  If  the  mov- 
ing body  is  propelled  at  a 
uniform  rate  of  one  hecto- 
metre to  the  minute,  this 
movement  can  be  expressed 
by  the  oblique  line  which  joins 
the  points  where  the  divisions  of  time  and  space 
intersect  (Fig.  25).  This  is  the  curve  of  movement. 
In  the  case  of  a  uniform  movement,  this  line  is 
always  straight :  but  it  will  be  more  or  less  obliquely 
inclined  according  to  the  speed  at  which  the  body 
travels.  Thus,  for  double  speed,  that  is  to  say,  two 
hectometres  in  the  minute,  the  line  will  pass  through 
the  point  at  which  the  second  division  of  space  and 
the  first  division  of  time  intersect.  It  will  thus  form 
the  diagonal  of  a  series  of  rectangles,  the  sides  of 
which  will  be  formed  of  two  space-divisions  and  one 
time-division.    This  system  of  representation  expresses 


Q  6 


\ 

| 

\ 

j 

I — J — 4—4 — i — - 

\       i 

i        'V 

Fig.  25. — Graphic  representation 
of  a  uniform  movement. 


36  MOVEMENT 

all  degrees  of  speed  and  all  kinds  of  movement.  A 
horizontal  line  signifies  a  period  of  rest,  and  the 
length  of  the  line,  or,  in  other  words,  the  number  of 
divisions  which  it  occupies,  is  a  measure  of  the 
duration  of  this  period  of  rest. 

Irregular  movement  is  expressed  by  a  curve,  the 
inclination  of  which,  i.e.  the  tangent,  indicates  from 
moment  to  moment  the  rate  of  progression.  Further, 
each  point  of  the  curve  indicates  according  to  its 
relation  to  the  horizontal  and  vertical  scales  the  time 
occupied  and  the  distance  travelled  since  the  com- 
mencement of  the  movemeat. 

Chart  of  a  Train  travelling  along  a  Line. — A 
geometrical  expression  for  all  sorts  of  movement  has 
become  now  almost  universal,  since  the  engineer  Ibry 
made  use  of  it  to  chronicle  the  progress  of  trains  along 
a  railway.  Nowadays  every  one  is  familiar  with  these 
charts,  in  which  are  to  be  seen  lines  intersecting  one 
another  in  all  directions.  Variations  both  as  regards 
inclination  and  direction  express  the  speed  and  the 
route  taken  by  all  trains  running  on  the  track. 
Fig.  26  is  an  example  of  such  a  chart  placed  by  the 
directorate  at  the  service  of  its  employes.  To  the 
left  of  this  chart,  along  the  axis  of  the  uprights,  are 
printed  in  series  the  names  of  the  various  stations. 
These  stopping-places  are  separated  on  the  chart  by 
intervals  proportional  to  the  number  of  kilometres 
which  actually  intervene  as  they  occur  on  the  line. 
In  the  horizontal  direction,  i.e.  along  the  axis  of  the 
abscissae,  time  is  registered  by  periods  of  an  hour; 
these  are  again  subdivided  into  periods  of  ten  minutes. 

To  indicate  that  a  train  should  arrive  at  a  given 
hour  at  a  particular  point  on  the  line,  its  position 
is  marked  on  the  chart  opposite  the  station  at  which 
it  is  expected,  and  vertically  above  the  division  which 
corresponds  to  the  time  at  which  it  is  due.     As  the 


MOVEMENT 


37 


train  proceeds  on  its  way  particulars  are  notified,  both 
as  regards  the  direction  in  which  it  is  going  and 
the  time  occupied.  But  if  the  train  stops,  its  place 
on  the  chart  only  changes  as  far  as  the  time-axis  is 
concerned,  and   consequently   the   stoppages   are   ex- 


FAR13 


Mor+t 
MONTERCAU 


"        MIDDAY 

Fig.  26.— Chart  to  express  the  movements  of  trains  along  a  railway.    (Ibry's  method.) 

pressed  by  horizontal  lines  more  or  less  elongated. 
The  inclination  of  the  line  expresses  the  speed  of 
tho  train.  The  faster  the  train  moves  the  more  nearly 
vertical  does  the  line  become.  Express,  fast,  through, 
and   stopping  trains  can   thus  be  distinguished  at  a 


38  MOVEMENT 

glance.  The  direction  of  the  curve  indicates  the 
destination  of  the  train.  Lines  descending  towards 
the  right  represent  trains  going  away  from  Paris, 
while  those  which  ascend  towards  the  right  correspond 
to  trains  going  towards  the  capital.  The  intersections 
of  lines  on  the  chart  signify  the  places  and  the  hours 
at  which  trains  cross  one  another  en  route.  This 
admirable  mode  of  representation  is  the  only  one 
which  should  be  employed  to  express  in  a  graphic 
form  the  trajectory  of  a  moving  point.  In  such  tables 
the  rate  of  progress  of  the  trains  is  supposed  to  be 
uniform,  and  is  represented  by  straight  lines  instead 
of  irregular  curves.  The  latter  are  employed  to 
express  a  change  of  speed  as  it  occurs  from  moment 
to  moment.  This  is  the  only  way  in  which  such  a 
mode  of  graphic  representation  deviates  from  what 
actually  occurs.  It  is  improbable,  however,  that  any 
serious  difficulty  would  arise  from  this  cause. 

The  Curve  of  a  Prolonged  Movement  should  be  re- 
corded in  Sections. — Charts  used  to  express  the  move- 
ments on  a  railway  are  crowded  with  detail,  because 
they  record  the  progress  of  every  train  which  moves 
in  one  or  other  direction  along  a  more  or  less  extensive 
section  of  the  line.  The  surface  of  the  paper  is  thi>s 
completely  utilized.  But  this  would  not  be  the  case 
if  we  had  to  record  the  progress  of  one  train  only 
during  a  long  run  extending  over  many  hours.  On 
referring  back  to  Fig.  25  it  will  be  noticed  that  the 
diagonal  of  the  square  expresses  a  journey  of  six 
hectometres  completed  in  six  minutes.  Now,  for  a 
journey  twice  as  long,  and  taking  twice  the  time,  the 
diagonal  would  be  double  the  length,  and  the  square 
containing  it  four  times  as  large.  According  to  this 
geometrical  progression,  we  should  have  to  use  a  sheet 
of  paper  a  metre  square  if  we  wanted  to  record  the 
progress   of  a  moving   body   for   twenty    kilometres. 


MOVEMENT 


39 


Time  in  minutes 
0'      f       2'      3'      »'.     S' 


E 

2   13 


10* 


And  this  immense  surface  would 
only  be  broken  by  a  single  fine 
line  dividing  it  diagonally  into 
two  parts.  This  inconvenience 
would  in  itself  serve  to  condemn 
the  method  from  a  practical  point 
of  view.  It  can  be  avoided,  how- 
ever, by  dividing  the  tracing 
into  sections,  each  of  which  ex- 
presses the  movement  during  a 
given  time.  Thus  Fig.  27  shows 
concentrated  on  a  narrow  strip 
of  paper  the  various  phases  of  a 
movement  which  otherwise  would 
have  required  a  surface  six  times 
as  large. 

On  this  strip  of  paper  the 
scale  representing  distance  is  con- 
tinuous, but  that  representing 
time  is  broken.  After  each  period 
of  five  minutes  the  curve  returns 
to  the  first  time-division,  but 
remains  on  the  distance-division 
at  which  it  has  actually  arrived. 
From  this  point  a  new  section 
of  the  curve  recommences.  The 
sections  A>  B,  C,  etc.,  thus  ex- 
press the  progress  of  the  moving 
body  over  a  distance  of  25  hecto- 
metres, and  during  a  period  of 
30  minutes,  and  the  curve  is 
quite  as  intelligible  as  would  be 
a  continuous  one  requiring  a 
large  surface  of  paper.* 

*  The    section    A    shows    that,    during    Fie.  27.— Successive  sections  of 
the  first  five   minutes,  the  moving  body        the  curve  of  a  movement. 


\A 

B 

\ 

\ 

\ 

sc 

sD 

V 

"s 

s 

X 

F 

\ 

< 

< 

IS 

^ 

i  . 

1 

15» 


IV 


25 


40  MOVEMENT 

How  a  Moving  Body  can  record  its  Own  Movement. — 
Poncelet  and  Morin  solved  this  problem  by  construct- 
ing the  well-known  machine  which  registers  the 
movement  of  a  falling  body.  In  this  machine,  the 
falling  body  is  provided  with  a  needle,  which  leaves 
its  record  on  paper,  and  moves  in  a  vertical  direction  at 
the  same  rate  as  the  falling  body.  Further,  the  paper 
rolled  round  a  revolving  cylinder  advances  in  a  hori- 
zontal direction  at  a  uniform  rate.  When  the  paper 
is  taken  off  the  cylinder,  the  needle  is  found  to  have 
traced  a  curve  which  is  parabolic  in  form.  This  is  the 
geometrical  manner  of  expressing  a  movement  of 
uniform  acceleration.  This  machine  is  a  type  of  the 
recording  apparatuses  of  which  there  are  nowadays  a 
considerable  number.  It  must  be  mentioned  at  the 
same  time  that,  by  reason  of  its  construction,  it  can 
only  record  the  curves  of  movement  to  actual  scale  ;  it 
could  not,  therefore,  be  used  to  represent  movements 
too  small  or  too  extensive  to  be  inscribed  on  a  sheet  of 
paper.  It  follows  that,  in  order  to  bring  the  propor- 
tions of  the  movement,  the  curve  of  which  is  to  be 
recorded,  within  convenient  proportions,  it  must  either 
be  enlarged  or  reduced. 

Proportional  Enlargement  and  Reduction  of  the  Re- 
corded Movement. — Very  feeble  movements,  such  as 
occur  in  living  organs,  and  such  as  physiologists  wish 
to  understand,  usually  have  to  be  immensely  enlarged. 
This  can  be  effected  by  levers  with  needles  fixed  to 

lias  traversed  a  distance  of  five  hectometres  at  a  uniform  rate. 
This  rate  is  maintained  for  two  minutes  longer  (section  B),  then 
a  stoppage  occurs  for  one  minute,  after  which  the  moving  hody 
again  advances  at  an  accelerated  pace  until  the  tenth  minute.  This 
speed  of  two  hectometres  a  minute  is  maintained  up  till  the  end 
of  the  eleventh  minute,  when  it  again  gives  place  to  a  slower  move- 
ment of  three  hectometres  in  four  minutes.  This  is  maintained 
during  section  D  and  part  of  E,  until  the  twenty-first  minute,  at  which 
a  period  of  rest  occurs.  This  stop  of  three  minutes,  which  is  continued 
during  section  F,  is  followed  by  another  period  of  uniform  movement 
during  which  the  speed  is  a  little  more  than  100  metres  per  minute. 


MOVEMENT 


41 


their  extremities.  It  is  in  this  way  that  the  arterial 
pulse,  as  it  alternately  raises  and  lowers  the  lever, 
demonstrates  in  different  patients  the  condition  of  the 
circulation.*  "When  a  movement  is  on  too  large  a 
scale  to  be  recorded  in   its   actual   size,  it   must  be 


v-JVvJV 


VlWiW/ 


^rvKNK 


Fig.  28. — Enlarged  tracings  of  the  pulse  in  different  diseases. 


reduced  before  transmission  to  the  recording  needle. 
There  are  several  ways  of  doing  this,  the  following  are 
the  most  usual  methods.  The  movement  can  be 
reduced  by  allowing  it  to  act  on  the  longer  arm  of  a 
lever,  while  the  writing  needle  is  placed  on  the  shorter. 

*  See  Tlie  Circulation.    Paris,  G.  Masscm,  1881. 


42  MOVEMENT 

The  relationship  which  obtains  between  the  lengths  of 
the  two  arms  determines  the  degree  to  which  the 
movement  is  reduced.  A  movement  can  be  uniformly 
reduced  by  means  of  an  indiarubber  thread ;  this  is  a 
convenient  method,  and  quite  reliable 
enough  for  most  purposes.* 

Let  c  b  (Fig.  29)  be  an  elastic  thread 
a.  as  nearly  homogeneous  as  possible.    Under 

the  influence  of  traction  it  will  become 
equally  extended  throughout  its  length. 
Let  us  make  fast  one  of  its  extremities,  c, 
by  means  of  a  nail,  for  instance.  If  we 
exercise  traction  at  the  other  end,  b,  so 
as  to  bring  it  to  b\  the  point  a  near  to  c 
will  only  travel  the  short  distance  aa'.  If 
we  have  fixed  the  tracing  needle  at  this 
point,  it  will  record  on  the  revolving 
cylinder  a  curve,  the  amplitude  of  which 
will  be  to  that  of  the  real  movement  as 
the  length  of  the  thread  ca  is  to  the 
length  cb. 

But    when    the    movement   has    to   be 

immensely  reduced,  as  happens  when  the 

path   of  a  body  moving  through  several 

Fic.29.-ProPor-  kilometres  has  to  be  traced  on  a  strip  of 

tiuna0V  a  move"  paper   a   few  centimetres   in   length,  the 

Sentany "nda-  movement  has   to  be   reduced  by   means 

rubber  thread.    of  ft  mechanical  arrangement  of  wheels. 

A  system  of  small  pinions  and  large  wheels  will 
effect  this  object ;  in  fact,  as  we  know,  it  will  indefi- 
nitely reduce  the  amplitude  of  any  movement.  We 
had  recourse   to  this  method   when  we  obtained  the 

*  This  method  of  reducing  the  curve  by  means  of  an  elastic  thread 
was  thought  of  by  Admiral  Paris  and  his  sou.  It  was  made  use  of  in 
their  apparatus  described  under  the  name  of  "Wave  Tracers." 
— Maritime  and  Culunial  Review,  June,  1867. 


MOVEMENT 


43 


curve  of  movement  presented  in  Fig.  27.  The  in- 
strument employed  in  this  experiment  is  applicable 
for  registering  the  progress  of  all  kinds  of  machines. 
It  is  called  an  "  Olograph." 

The    Odograph.  —  Fig.  30   represents   a    pedestrian 


Fig.  30.— Pedestrian  pushing  an  odograph  in  front  of  him. 

pushing  before  him  a  light  species  of  wheelbarrow. 
The  track  of  the  wheel  upon  the  ground  represents 
the  distance  traversed.  The  wheel  of  the  barrow,  by  a 
system  of  reducing  wheels,  controls  the  movement  of  a 
strip  of  paper.  Further,  a  tracing  needle  worked  by  a 
clock  moves  across  the  paper  at  any  desired  rate.     A 


u 


MOVEMENT 


time-curve  of  the  distance  traversed  results  from 
the  combination  of  these  two  movements.  Figs.  31 
and  32  show  the  details  of  the  apparatus.  A  strip  of 
paper,  the  length  of  which  is  about  one  metre,  passes 
between  cylindrical  rollers  which  advance  it  a  distance 
proportional  to  the  space   traversed   by   the   moving 


Kir..  31. — Detaib  of  the  odograph.  The  strip  of  paper,  which  has  already  received 
a  tracing  of  progression  and  re.-t,  can  be  clearly  ?een  in  position.  One  needle  has 
completed  its  journey,  and  a  second,  in  iis  turn,  is  just  about  to  commence. 
The  needles,  to  the  number  of  five,  are  arranged  at  a  distance  of  six  centimetres 
from  one  another,  along  a  steel  band  which  passe*  round  the  two  rollers  G  by 
mea>  s  of  clockwork.  At  B  can  be  seui  the  extremity  of  the  shaft  which  imparts 
the  movement  to  the  rollers. 

body.  Each  revolution  of  the  wheel,  representing  a 
distance  of  three  metres,  will  advance  the  wheel  of  the 
cylindrical  rollers  through  a  distance  of  one  cog.  This 
is  effected  by  means  of  a  crank  which  runs  along  one 
of  the  handles  of  the  wheelbarrow.     During  this  time 


MOVEMENT  45 

the  strip  of  paper  will  have  progressed  a  very  short  dis- 
tance, 0*1  millimetre  for  instance.  It  will  have  com- 
pletely passed  through  the  rollers  at  the  end  of  a  run  of 
30  kilometres.  The  needle,  which  writes  on  the  paper, 
is  made  of  brass,  and  the  paper  itself  is  coated  with  a 
layer  of  white  zinc,  and  called  "papier  couche"  in  the 


Fig.  32. — The  instrument  is  seen  obliquely  from  behind.  The  dial  of  the  clock  is 
visible.  The  strip  of  paper  is  in  position  between  the  rollers,  and  the  needle  is  in 
the  act  of  tracing.  The  teeth  of  the  comb  have  already  imprinted  hourly  sub- 
divisions on  the  paper.  At  B  the  end  of  the  shaft  acts  by  means  of  a  clapper  on 
a  ratchet-wheel,  which  iu  its  turn  controls  the  movement  of  the  rollers  by  means 
of  aa  endless  screw. 

trade.  On  this  latter  the  brass  leaves  a  very  fine  and 
clearly  defined  track.  It  never  wears  out  like  a  pencil, 
neither  does  it  require  ink  like  a  pen.  To  obtain  a 
curve  of  the  movement,  the  needle  must  have  imparted 
to  it  a  uniform  motion  by  means  of  clockwork,  and  it 
5 


46  MOVEMENT 

must  traverse  the  width  of  the  paper  in  one  hour. 
Besides  this,  as  the  strip  of  paper  is  drawn  through 
the  rollers,  it  passes  beneath  a  comb,  which  registers 
equidistant  lines  along  the  length  of  the  paper; 
the  distance  between  two  teeth  corresponds  to  a 
duration  of  ten  minutes.  This  greatly  facilitates  the 
reading  of  the  distance  traversed  in  a  particular  time. 
Thus  during  every  hour  the  needle  traces  a  section  of 
a  curve  analogous  to  those  in  Fig.  27,  and  which  are 
distinguished  in  order  by  the  letters  A,  B,  C,  —  F, 
because  the  needle  takes  exactly  one  hour  to  cross  the 
width  of  the  paper.  As  soon  as  the  first  curve  has 
been  registered  another  one  is  commenced,  because  a 
second  needle  in  turn  begins  to  register,  and  at  the 
third  hour  another  needle,  and  so  on  indefinitely  during 
the  whole  of  the  journey.*  When  the  strip  of  paper 
ceases  to  advance,  during  periods  of  rest,  the  clock 
nevertheless  continues  to  move  the  needle,  and  the 
latter  describes  a  straight  line  at  right  angles  to  the 
long  axis  of  the  paper.  This  way  of  registering  move- 
ment is  identical  with  that  which  was  designed  by 
Ibry.  We  believe  that  odography  could,  with  a  few 
special  modifications,  be  applied  for  registering  the 
progress  of  a  railway  train.  A  novel  arrangement  of 
pneumatic  tubes  can  transmit  each  revolution  of  the 
wheels  of  the  engine  to  the  mechanism  of  the 
cylindrical  rollers,  and  thus  an  odograph  can  be 
placed  in  each  compartment,  and  supply  continuous 
information  of  the  progress  of  the  train.  Thanks  to 
the  kindness  of  M.  Millet,  chief  engineer  of  the  loco- 
motive department  on  the  Southern  Railway  (Chemin 
de  fer  du  Midi),  we  were  able  to  try  the  effect  of  the 
odograph  on  express  trains  running  from  Dax  to 
Bordeaux,  and  vice  versa.     Fig.  33  shows  in  column  A 

*  The  needles  are  driven  by  an  endless  steel  band  controlled  by 
the  clock. 


Fig.  33.— Two  odographic  cliaits  expre^inK.  accord  ng  to  different  scales,  the  advance 
of  a  fast  train. 


48  MOVEMENT 

a  section  of  the  original  chart  taken  on  one  of  these 
journeys  between  Dax  and  Moncenx.  To  measure 
from  moment  to  moment  the  rate  of  travelling,  a  small 
divided  scale  can  be  applied  to  the  corresponding  part 
of  the  diagram.  By  means  of  this  scale  we  can 
measure  the  length  of  any  portion  of  the  curve,  which 
corresponds  to  the  distance  traversed  in  ten  minutes. 
In  this  case  it  can  be  seen  that  the  speed  was  55 
kilometres  per  hour.  These  charts  are  exactly  like 
those  employed  by  railway  companies ;  the  method  of 
expressing  periods  of  progression  and  rest  is  the 
same  throughout,  the  only  difference  is,  that  Ibry's 
charts  were  theoretical,  i.e.  the  speed  of  the  trains 
is  supposed  to  be  uniform,  and  is  represented  by 
straight  lines,  and  in  ours  the  actual  speed  is  experi- 
mentally found,  and  expressed  by  variations  more  or 
less  pronounced.  It  can  be  seen  that  from  Dax  to 
Eion,  and  from  Rion  to  Moncenx,  the  line  is  not 
straight  but  slightly  curved,  which  means  that  there 
is  a  slight  variation  in  the  speed.  It  is  generally 
immediately  before,  or  immediately  after,  a  stoppage 
that  these  variations  are  noticeable.  At  the  moment 
that  the  train  comes  to  a  stop,  the  curve  suddenly 
changes  its  direction,  which  indicates  that  under  the 
influence  of  the  brake  there  is  a  rapid  transition  from 
a  high  rate  of  speed  to  a  condition  of  rest.  On  the 
contrary,  at  the  moment  of  departure,  the  curve 
describes  a  parabola,  which  indicates  how  gradual  is 
the  acceleration,  and  how  slowly  the  train  gets  up 
speed.  The  movement  of  the  paper  must  be  con- 
siderably slowed  down,  if  we  want  to  inscribe  all  the 
phases  of  a  long  journey  within  the  limits  of  a  single 
sheet  of  paper.  Column  B  was  obtained  in  this  way, 
and  on  it  is  registered  a  journey  from  Dax  to  Bordeaux, 
representing  a  distance  of  GO  kilometres. 

In  odography  the  movement  of  the  paper  should  be 


MOVEMENT  49 

regulated  to  suit  the  average  speed  of  the  conveyance 
the  movement  of  which  is  to  be  ascertained,  be  it 
carriage,  locomotive,  or  boat,  etc.*  Wide  as  is  the 
range  of  movements  capable  of  being  recorded  by 
mechanical  means,  nevertheless  there  are,  as  we  re- 
marked before,  cases  in  which  this  method  ceases  to  be 
applicable.  It  will  be  seen  how  valuable  the  employ- 
ment of  photography  becomes  in  cases  of  this  kind. 

Photography  of  the  Movements  of  Lippmann's  Electro- 
meter.— In  1877,  our  colleague  and  friend  Lippmann 
had  just  invented  his  capillary  electrometer,  an  in- 
strument so  marvellously  sensitive  that  it  was  capable 
of  registering  the  slightest  electrical  variation  that 
occurred  in  living  tissues.  But  for  this  purpose  it  was 
necessary  to  make  this  electrometer  a  recording  instru- 
ment.    This  was  managed  by  means  of  photography. 

As  the  column  of  the  electrometer  is  exceedingly 
fine,  the  movements  must  be  observed  under  the 
microscope. 

This  column  presents  totally  different  appearances 
under  different  conditions  of  illumination ;  on  a  light 
background  it  appears  as  a  dark  line ;  on  a  dark  back- 
ground, when  illuminated  from  the  sides,  it  stands  out 
as  a  very  bright  line.  This  column  is  seen  to  elongate 
and  contract  according  to  the  direction  and  the  in- 
tensity of  the  current  acting  upon  it.  By  receiving 
its  image  on  a  photographic  plate  a  very  intense  black 
line  will  be  obtained.  If  the  sensitive  plate  is  moved 
at  a  uniform  rate  at  right  angles  to  the  axis  of  the 
column,  all  its  variations  in  length  will  be  apparent 
in  the  image. 

The  effect  of  moving  the  plate  is  that  the  image 
of  the  column  is  no  longer  a  simple  line ;  it  is  spread 
out  in  the  form  of  a  band,  the  sinuous  border  of  which 

*  For  the  details  of  the  employment  of  odography,  see  La  Nature, 
No.  278,  September  28,  1878. 


50  MOVEMENT 

corresponds  to  the  variations  in  the  length  of  the 
column  of  mercury. 

To  illuminate  the  column  of  this  instrument,  we 
used  a  series  of  flashes  from  an  induction  coil  furnished 
with  a  condenser.  This  intermittent  illumination  dis- 
turbed the  continuity  of  the  images,  and  thus  a  series 
of  bright  lines  of  unequal  length  was  produced. 

By  this  means  tracings  can  be  obtained  to  demon- 
strate the  electrical  changes  in  the  hearts  of  tortoises 
or  frogs,  as  they  occur  respectively  during  the  periods 
of  systole  and  diastole. 

The  sinuous  border  representing  the  summit  of  the 
column  of  mercury  in  such  a  tracing  has  a  very  close 
resemblance  to  the  curve  obtained  by  mechanically 
registering  the  actual  movements  of  the  heart  during 
its  various  phases.  The  heart,  like  all  other  muscular 
structures,  shows  changes  in  its  electrical  condition, 
according  as  it  is  contracted  or  relaxed. 

Determination  by  Means  of  Chronophotography  of  the 
Movement  executed  by  a  Falling  Body. — In  the  study 
oh  movement,  photography  has  the  advantage  of  not 
being  obliged  to  borrow  any  motive  power  from  the 
object  observed.  The  following  experiment  may  be 
made.  A  black-velvet  curtain  may  be  hung  vertically 
so  as  to  form  a  dark  screen,  in  front  of  which  a  white 
ball,  lit  up  by  the  sun's  rays,  is  allowed  to  fall.  A 
divided  scale  is  placed  vertically  in  front  of  the  dark 
background,  to  measure  the  distance  traversed.  A 
chronometric  dial  is  used  to  measure  the  intervals 
between  the  successive  images. 

When  the  circular  diaphragm  has  acquired  the 
desired  velocity,  an  assistant  pulls  the  string  and  the 
ball  falls.  The  photographic  plate  receives  a  series  of 
images  of  this  ball,  showing  the  positions  it  occupies 
at  each  successive  exposure.  In  this  way  all  the 
necessary  elements  are  obtained  for  determining  "  the 


MOVEMENT 


51 


laws  of  motion."  In  order  to  make  it  more  easy 
to  take  measurements  from  this  photograph,  the 
original  plate  is  enlarged,  and  the  different  positions 
of  the  falling  body  are  obtained  on  a  convenient  scale. 
Let  us  draw  a  horizontal  tangent  to  the  ball  in  each 
of  its  positions.  The  distances  fallen  during  the  various 
periods  since  the 
commencement  of 
the  fall  will  then 
be  seen  in  series, 
and  it  will  be  ob- 
served that  these 
distances  increase 
as  the  square  of  the 
time.  For  instance, 
the  distance  tra-» 
versed  during  the 
second  period  of 
fall,  that  is  to  say, 
after  the  second 
exposure,  is  four 
times  as  much  as 
that  which  was  tra- 
versed in  the  first 
period. 

If  one  wishes  to 
construct  a  time- 
curve  of  the  dis- 
tance traversed,  the  sheet  of  paper  should  be  divided 
by  vertical  lines  at  equal  distances.  At  the  inter- 
sections of  each  of  these  lines  with  the  horizontal 
tangents  a  mark  is  made  (a  dot  in  the  centre  of  a 
circle).  The  curve  E,  which  joins  all  of  these  marks, 
is  a  parabola,  and  represents  the  time-curve  of  a  body 
moving  at  an  uniformly  accelerated  rate. 

The  curve  of  velocity  can  be  constructed  by  marking 


Fig.  34.— Photography  of  the  movement  of  a  falling 
body. 


of   '    ! 

X 

A 

W      "^     "  ■" 

Q 

V'    ■: 

q:-:::::" 

Ql 

Q     

Q 

Q_  1  __ 

Q 1 

E 

Q.  1         1 

Ql       1 

Q 

Ql 

Q 

Qv_  J_L    __ 

— 1 LJ 1 — 1      1     1*4  \ 

Fig.  :$5.— Curves  of  tlio  movement  of  a  falling  body. 


MOVEMENT  53 

off  from  each  time-division  a  distance  which  represents 
the  space  traversed  by  the  ball  in  the  corresponding 
interval  of  time.  The  small  crosses  mark  the  lengths 
of  such  a  series  of  ordinates.  Taken  together  they 
form  the  line  V,  which  is  the  curve  of  velocity.  Such 
a  line  is  a  straight  one,  but  obliquely  inclined,  and 
expresses  a  velocity  of  uniform  increment. 

Finally,  the  curve  of  acceleration  is  obtained  by 
marking  off  on  the  ordinates,  under  each  of  the  time- 
divisions,  the  excess  of  velocity  of  each  period  over 
and  above  that  of  the  one  which  precedes  it,  that  is 
to  say,  the  excess  of  the  second  over  the  first,  and 
the  third  over  the  second ;  in  other  words,  the  incre- 
ment of  velocity,  or  acceleration,  in  a  series  of  time 
intervals.  A  large  black  dot  marks  the  length  of  each 
of  these  ordinates  ;  the  dots  united  together  by  the 
line  A  constitute  a  straight  horizontal  line  showing 
the  acceleration  was  uniform.* 

In  constructing  these  figures,  the  unit  of  time  was 
represented  as  any  interval.  This  method  answers 
very  well  in  comparing  the  relative  degrees  of  speed 
and  acceleration  ;  but  to  ascertain  the  exact  degree, 
these  indefinite  intervals  must  represent  a  second,  the 
recognized  unit  of  time. 

The  chronometric  dial  provides  us  with  the  means 
of  doing  this  in  the  same  manner  as  the  divided  scale 
measured  in  meters  and  fractions  of  meters  the  space 
traversed  by  a  falling  body.  Thus  chronophotography 
provides  us  with  the  means  of  constructing  the  curves 
of  movement. 

*  On  account  of  a  mistake  in  the  diagram  (Fig.  35),  the  degree  of 
acceleration  is  half  what  it  ought  to  be. 


CHAPTER  IV 
CIIKONOPIIOTOGRAPHY   ON   FIXED   PLATES 

Summary. — Object  of  chronophotograpliy;  principles  of  the  method: 
measurement  of  time  and  space — Influence  of  the  extent  of 
surface  covered  by  the  object  which  is  to  be  photographed; 
influence  of  the  rate  of  movement— Geometrical  chronophoto- 
graphy — Stereoscopic  chronophotograpliy— Method  of  multiply- 
ing the  number  of  images  without  producing  confusion — Alter- 
n.ting  images  -  Separation  of  the  images  on  the  photographic 
plate;  separation  by  moving  the  apparatus — Separation  by  em- 
ploying a  revolving  mirror. 

Since  the  object  of  chronophotograpliy  is  to  determine 
with  exactitude  the  characters  of  a  movement,  such  a 
method  ought  to  represent  the  different  positions  in 
space  occupied  by  a  moving  object,  i.e.  its  trajectory, 
as  well  as  define  the  various  positions  of  this  body  on 
the  trajectory  at  any  particular  moment. 

Let  us  suppose  that  an  ordinary  photographic  camera 
is  directed  towards  a  dark  background,  that  the  lens 
is  uncovered,  and  that  a  ball,  brightly  illuminated  by 
the  sun,  is  thrown  across  the  field  of  the  objective. 
During  its  passage  this  ball  leaves  an  impression  on 
various  parts  of  the  sensitized  plate,  and  on  examining 
the  plate  there  is  found  a  continuous  curved  line  which 
exactly  represents  the  path  taken  by  the  luminous 
ball  (upper  curve,  Fig.  36). 

If  we  repeat  this  experiment,  but  only  admit  light 
into  the  dark  chamber  in  an  intermittent  fashion,  and 


CHRONOPHOTOGRAPHY  ON  FIXED  PLATES   55 

at  regular  intervals  of  time,  an  interrupted  trajectory 
will  be  obtained  (lower  curve,  Fig.  36).  This  repre- 
sents the  successive  positions  assumed  by  the  moving 
object  at  each  moment  when  light  is  admitted.  This 
is  the  chronophotographic  trajectory  In  this  method 
the  intervals  of  time  separating  two  images  are  of 
constant  and  known  duration. 

To  obtain  the  best  possible  results,  the  object  must 
be  brightly  illuminated  and  the  background  absolutely 
dark.  The  duration  of  the  exposure  must  be  very 
brief,  in  order  that  the  object  may  not  move  an  ap- 
preciable distance  during  a  single  admission  of  light. 


Fig.  36. — Simple  trajectory  and  chronophotographic  trajectory  of  a  bright  ball 
moving  in  front  of  a  dark  background. 

The  original  form  of  the  chronophotographic  appa- 
ratus was  very  simple.  It  consisted  of  an  ordinary 
camera  and  lens.  Within  the  body  of  the  camera,  in 
front  of  the  plate,  a  fenestrated  diaphragm  was  fixed. 
This  rotated  at  a  perfectly  uniform  rate  by  means  of 
a  crank  and  regulator.  The  sensitized  plate  was  held 
in  a  frame  and  fixed  in  a  position  so  that  the  object 
was  focussed  accurately  upon  it.  As  each  slit  in  the 
diaphragm  came  into  position,  the  plate  received  an 
impression  of  the  illuminated  object,  representing  the 
actual  form  and  position  of  the  object  at  that  particular 
moment.  Now,  as  the  object  became  displaced  between 
successive  exposures,  a  series  of  impressions  was  ob- 
tained exactly  corresponding  to  the  shape  and  position 


56  MOVEMENT 

of  the  object  in  the  various  phases  of  motion.  The 
interval  between  each  image  was  exactly  ^0  of  a  second, 
and  the  duration  of  the  exposure  5^$  of  a  second.  A 
metre  rule  with  very  clearly  defined  divisions  was 
placed  in  front  of  the  screen,  and  in  the  same  plane 
as  the  object.  The  image  of  this  rule  reproduced  on 
the  sensitized  plate  served  as  a  scale  to  measure  the 
real  size  of  the  object,  and  the  spaces  traversed  during 
each  period  of  j1^  of  a  second. 

Instead  of  depending  on  the  absolute  regularity 
of  the  movement  of  the  diaphragm  as  a  means  of 
measuring  the  time  relations,  it  would  be  better  in 
experiments  requiring  great  accuracy  to  make  use  of 
the  chronometric  dial  (Chap.  I.,  Fig.  12).  Thus  in  the 
experiments  on  falling  bodies  described  on  page  51, 
the  intervals  of  time  between  two  successive  exposures 
were  measured  by  the  angular  distance  through  which 
the  needle  moved  between  two  successive  images. 
This  proceeding,  like  that  in  which  the  tuning  fork  is 
employed  as  a  mechanical  means  of  registering  the 
rate  of  movement  of  the  paper,  permits  of  the  diaphragm 
revolving  at  any  speed  required.  The  degree  of  speed 
can  always  be  ascertained  by  referring  to  the  position 
of  the  needle  on  the  dial. 

As  for  the  measurement  of  space,  the  image  of  a 
divided  scale  serves,  as  we  said,  for  measuring  the 
various  distances  on  the  photographic  plate. 

But,  since  all  measurements  made  from  a  reduced 
scale  necessitate  a  series  of  calculations  before  the 
real  dimensions  are  ascertained,  it  is  very  desirable  to 
find  some  means  of  avoiding  these  tedious  calculations. 
This  may  be  done  by  enlarging  the  images,  by  means 
of  a  projection  lantern,  until  the  object  assumes  its 
actual  dimensions,  i.e.  until  the  measuring  scale  on  the 
screen  appears  to  be  exactly  one  metre  in  length.  In 
this  case  all  the  dimensions  of  the  image  can  be  directly 


CHRONOPHOTOGRAPHY  ON  FIXED  PLATES   57 

measured.  Such  chronophotographic  pictures  contain 
the  two  necessary  elements  for  understanding  a  move- 
ment, namely,  a  notion  of  space  as  well  as  that  of 
time ;  nevertheless,  as  we  shall  see,  it  is  often  difficult 
to  harmonize  two  such  incompatible  notions  without 
having  recourse  to  certain  expedients. 

Influence  of  the  Extent  of  Surface  covered  by  the 
Moving  Object. — If  the  object  under  observation  covers 
only  a  small  surface  in  the  direction  of  movement,  a 
large  number  of  images  may  be  obtained  without  super- 
position or  confusion,  as,  indeed,  we  noticed  in  the  case 


Fig.  37.— A  man  walking.     Cbruiiophotograi>hy  on  a  fixed  plate. 

of  the  moving  ball.  As  far,  then,  as  time  is  concerned 
we  have  a  very  complete  picture,  whereas  that  of  space 
is  very  restricted. 

Now,  if  we  take  a  series  of  images  of  a  man  walking, 
the  question  of  space  becomes  a  most  complicated  one. 
Each  image  must  be  spread  over  a  considerable  surface 
if  it  is  to  show  the  various  positions  assumed  by  the 
head,  arms  and  legs.  Now,  the  larger  the  space  covered 
by  the  image,  the  smaller  must  be  the  number  that 
can  be  taken  on  one  plate  without  superposition  and 
confusion.     With  a  lar^e  animal,  a  horse  for  instance, 


58 


MOVEMENT 


the  number  of  images  has  to  be  very  limited,  for  the 
length  of  each,  measured  in  the  direction  of  movement, 
is  so  great  that  they  readily  overlap,  as  in  Fig.  38. 


Fig.  38.— Arab  horse  at  a  gallop.     The  large  surface  covered  by  e.  «.h  image  cause 
almo.it  complete  superposition. 

Influence  of  the  Rate  of  Movement. — In  different 
speeds  of  translation,  the  number  of  images  which  can 
be  taken  in  a  given  time  without  producing  confusion, 
increases  as  the  former  become  greater.  This  may 
be  proved  by  comparing  a  series  of  images  of  a  runner 
(Fig.  39)  with  those  of  a  man  merely  walking  (Fig.  37). 


FlG.  o9.  -  A  man  ruimuig.     Uuiunop.iutogrupliy  on  ;i  fixed  plate. 

The  figures  of  the  runner  are  much  further  apart, 
although  the  frequency  of  exposure  is  the  same  in  both 
cases.  If  the  runner  were  to  come  to  a  standstill,  the 
images  would  become  superimposed.     Sometimes  such 


CHRONOPHOTOGRAPHY  ON  FIXED  PLATES   59 

a  superposition  of  images  can  be  put  to  practical  use. 
Thus  it  gives  greater  intensity  to  those  images  which 
represent  the  movements  of  least  rapidity.  One  of 
the  very  first  applications  of  photography  to  the  study 
of  movement  was  suggested  by  Messrs.  Onimus  and 
Martin,  in  the  year  1865.  These  investigators  exposed 
the  heart  of  a  living  animal,  and  took  a  photograph  of 
it  by  leaving  the  lens  permanently  uncovered.  The 
photograph  was  found  to  have  a  double  outline  repre- 
senting the  two  extreme  positions  of  contraction  and 


Fig.  4P.— A  boxer  represented  in  the  two  extreme  portions  of  a  movement. 

dilatation.  At  these  two  periods  the  heart  remains 
momentarily  motionless,  and  its  configuration  is 
imparted  to  the  sensitized  plate,  whereas  no  clear 
impression  is  left  of  it  during  the  intermediate  phases 
of  motion. 

Mr.  Demeny  had  recourse  to  this  method,  which 
had  fallen  into  unwarranted  oblivion,  and  with  which 
even  he  himself  was  previously  unfamiliar.  In  study- 
ing physical  exercises,  he  took  the  photograph  of  a 
man  in  the  act  of  boxing  in  front  of  a  dark  screen. 


60 


MOVEMENT 


His  photograph  showed  two  particular  attitudes  clearly 
defined,  and  from  them  Fig.  40  was  produced ;  the 
latter  shows  the  boxer  preparing  for  a  movement,  and 
his  position  immediately  after  completing  it.  The 
intermediate  phases  of  movement  were  so  rapid  that 
they  left  no  appreciable  impression  on  the  plate. 


mMm 


Fig.  41. — Man  dressed  in  black,  with  white  linf-s  and  points  for  the  chronophotographic 
study  of  the  movement  of  the  important  parts  of  the  body. 

Geometrical  Chronophotography. — This  confusion  from 
the  superposition  of  images  sets  a  limit  to  the  applica- 
tion of  chronophotography  on  fixed  plates,  yet  in 
many  cases,  by  means  of  certain  appliances,  this 
difficulty  may  be  overcome.     The  most  obvious  method 


CHEOXOPHOTOGEAPHY  ON  FIXED  PLATES   61 

consists  in  artificially  reducing  the  surface  of  the 
object  under  observation.  Such  parts  of  the  object 
as  are  not  wanted  in  the  photograph  are  blackened 
and  thus  rendered  invisible  ;  on  the  other  hand,  those 
portions,  the  movements  of  which  are  to  be  studied, 
are  picked  out  in  white.  Thus  a  man  dressed  in  black 
velvet  (Fig.  41),  with  bright  stripes  and  spots  on  his 
limbs,  is  reproduced  in  the  photograph  as  a  system  of 
white  lines,  which  indicates  the  various  positions 
assumed  by  the  limbs.     In  the  diagram  thus  obtained 


Fig.  42.— Images  of  a  runner  reduced  to  a  system  of  bright  lines  for  representing  the 
position  of  his  limbs.     (Geometrical  chronophotography.) 

(Fig.  42),  the  number  of  images  may  be  considerable, 
and  the  notion  of  time  very  complete,  while  that  of 
space  has  been  voluntarily  limited  to  what  was  strictly 
necessary. 

Stereoscopic  Chronophotography.  —  In  Chapter  II. 
we  discussed  the  method  of  obtaining  stereoscopic 
pictures  of  figures  described  by  straight  or  curved 
lines  moving  in  space.  A  series  of  separate  images 
was  thus  obtained,  that  is  to  say,  they  were  produced 
by  intermittent  exposure  of  the  objective.  This  was 
done  with  the  double  object  of  explaining  the  method 
of   producing   figures  in   relief,  and   of  showing   the 


62  MOVEMENT 

successive  positions  occupied  by  the  line  which  en- 
gendered them.  Now,  if  the  intervals  between  the 
exposures  are  precisely  equal,  we  have  an  example  of 
stereoscopic  chronophotography,  and  consequently  a 
complete  expression  of  the  movement.  This  method 
is  applicable  in  a  great  many  cases  in  which  we  want 
to  know  whether  the  moving  object  moves  in  one 
plane  only  or  in  three. 

Method  of  multiplying  the  Number  of  Images  without 
producing  Confusion. — The  applications  of  chrono- 
photography are,  as  we  have  seen,  limited  by  inter- 
ference from  superposition  and  consequent  confusion. 
Now,  the  larger  the  space  covered  by  the  object,  and 
the  slower  the  movement,  the  sooner  does  superposition 
occur.  Thus,  if  the  space  is  large  and  the  movement 
slow,  recourse  must  be  had  to  certain  measures,  if  we 
want  to  obtain  a  photograph  of  the  various  positions 
occupied  in  space. 

One  method  consists  in  taking  alternating  images, 
another  in  separating  the  images  on  the  plate  by 
making  them  fall  on  different  parts. 

Alternating  Images. — To  obtain  these,  a  stereoscopic 
apparatus  with  two  lenses  is  employed,  both  of  which 
are  controlled  by  the  same  diaphragm.  Such  a 
diaphragm  should  be  circular,  and  contain  only  one 
slit,  which,  as  it  rotates,  alternately  admits  the  light 
first  by  the  right  and  then  by  the  left  lens.  Two 
series  of  images  will  be  thus  obtained,  which  lie  in  two 
parallel  lines.  The  upper  series  corresponds  to  the 
odd  numbers,  and  the  lower  to  the  even  numbers,  as 
is  shown  below — 

13         5         7         9 
2        4        6         8         10 

In  this  way  Fig.  43  was  obtained,  which  shows  the 
various  positions  of  the  wings  as  assumed  by  a  seagull 
during  flight. 


CHROXOPHOTOGRAPHY  OX  FIXED  PLATES    63 

Only  five  different  positions  can  be  represented  in  a 
single  series  without  confusion.  Now,  thanks  to  the  two 
series,  which  are  the  compliments  of  each  other,  the 
number  of  images  is  doubled,  and  the  succession  of 
movements  represented  by  them  can  be  followed  by 
passing  alternately  from  the  odd  to  the  even  number 
in  the  natural  order,  as  is  indicated  by  the  small  arrows 
in  the  diagram. 


Fig.  43. — Alternating  images  for  multiplying  the  number  of  positions  afforded  by 
chronopbotography. 


It  is  almost  unnecessary  to  add  that  these  images  do 
not  constitute  a  stereoscopic  series,  for  they  are  taken 
successively,  and  the  single  slit  of  the  diaphragm  never 
exposes  mure  than  one  of  the  two  photographic  plates. 

Separation  of  the  Images  on  the  Photographic  Plate. — 
When  the  object,  of  which  successive  images  are  to  be 
taken,  confines  its  movements  to  one  particular  spot, 
confusion  and  superposition  are  bound  to  occur.     This 


64  MOVEMENT 

difficulty,  however,  can  be  overcome  by  a  variety  of 
expedients,  one  of  which  is  already  known  to  us,  and 
which  depends  on  the  horizontal  and  forward  move- 
ment of  the  photographic  plate. 

In  speaking  of  the  photographic  registration  of 
the  variation  of  Lippmann's  electrometer,  we  showed 
how  successive  images  of  the  illuminated  column  of 
mercury  formed  a  continuous  series,  owing  to  the 
onward  movement  of  the  plate.  This  mode  of  repre- 
senting the  various  phases  of  electrical  variation  is 
entirely  comparable  to  the  mechanical  registration  of 
a  movement  by  means  of  a  needle  which  traces  its 
record  on  a  moving  strip  of  paper.  This  kind  of 
separation  would  be  applicable  in  a  great  number 
of  cases  if  it  did  not  require  a  special  and  rather 
complicated  apparatus,  namely,  that  of  a  movable 
slide  and  a  clockwork  motor.  But  with  an  ordinary 
apparatus  a  similar  separation  can  be  obtained  by 
imparting  an  onward  movement  to  the  image  itself 
while  the  photographic  plate  remains  in  position.  In 
order  to  effect  this,  a  rotatory  movement  round  its 
own  axis  must  be  communicated  to  the  apparatus 
itself  between  the  periods  of  exposure.  The  principal 
optical  axis  of  the  objective  is  thus  displaced  in  a 
horizontal  plane ;  and  the  image  of  a  man  standing 
in  front  of  the  dark  screen  will  consequently  be 
displaced  in  a  corresponding  direction  on  the  plate 
itself.  If  this  man  executes  certain  movements  in 
the  same  spot,  thus  constituting  a  variety  of  attitudes, 
or  if  he  advances  excessively  slowly,  his  successive 
attitudes,  instead  of  being  confused  and  superimposed, 
will  constitute  a  series  of  disconnected  images,  ranged 
side  by  side,  as  if  he  were  moving  at  a  moderate 
pace  in  a  horizontal  direction  in  front  of  the  dark 
screen. 

But  it  may  be  urged  that  the  conception  of  space 


CHRONOPHOTOGRAPHY  ON  FIXED  PLATES   65 

is  false,  because  a  variety  of  attitudes  on  the  same 
spot  are  reproduced  in  the  photograph  as  if  they 
were  onward  movements.  The  real  position  of  each 
movement  must  be  located  in  the  diagram.  This  can 
be  done  in  the  following  way  : — By  the  side  of  a  man 
jumping  about  on  the  same  spot,  or  walking  slowly, 
a  white  and  perfectly  motionless  object  is  placed  just 
in  front  of  the  dark  background.  The  images  of  this 
object  will  be  arranged  in  a  consecutive  series  on  the 


Fig.  44.— Rotating  mirror  for  separating  the  images  of  an  object  which  moves  too 

slowly. 


plate.  Xow,  as  it  is  known  that  these  positions  corre- 
spond to  a  fixed  point,  they  serve  as  a  means  of 
estimating  the  real  positions  occupied  by  the  man  at 
the  time  of  each  exposure.  Such  a  movement  im- 
parted to  the  apparatus  is  a  very  simple  means  of 
obtaining  a  consecutive  series  of  chronophotographic 


66  MOVEMENT 

images,  but  it  is  difficult  to  ensure  perfect  regularity 
of  movement.* 

A  better  method  of  producing  the  same  result 
consists  in  reflecting  the  image  of  the  object  by 
means  of  a  revolving  mirror.  The  image  thus  be- 
comes deflected  before  it  enters  the  camera.  The 
mirror,  silvered  by  Foucault's  method,  rotates  on  a 
vertical  axis,  and  by  means  of  clockwork  it  is  easy 
to  ensure  a  uniform  movement.  Any  speed  that  is 
desired  can  be  obtained. 

By  these  different  ways  of  separating  the  image, 
the  range  of  chronophotography  on  fixed  plates  can 
be  considerably  extended.  For  thus  we  are  enabled 
to  record  movements  executed  on  the  same  spot,  or 
of  extreme  degrees  of  slowness.  At  the  same  time 
the  method  ceases  to  be  applicable  when  the  duration 
of  the  movement  is  greatly  prolonged,  when  a  large 
number  of  images  are  required,  or  when  the  dimensions 
of  the  plate  will  not  contain  the  images.  Neither  is 
it  applicable  when  the  moving  object  is  dark  and  the 
background  light.  Recourse  must  then  be  had  to 
a  new  method.  This  is  chronophotography  on  a 
moving  plate ;  it  will  be  described  further  on. 

*  Another  inconvenience  presented  by  this  method  is  that  there  is 
a  risk  of  the  apparatus  itself  introducing  a  source  of  error.  For  the 
circular  diaphragm  rotating  at  a  y:reat  rate  tends  to  preserve  its  own 
plane  of  rotation,  and  consequently  to  become  distorted  when  exposed 
to  sudden  movement. 


CHAPTER   V 

DESCRIPTION    OF    THE    APPARATUS 

Summary. — Construction  of  the  apparatus — Slide,  object-glass,  ciroular 
diaphragms — Erection  of  the  dark  background  at  the  physiological 
station — Dark  background  for  photographing  objects  in  water — 
Photography  of  light  objects  in  darkness  or  in  a  red  tight — Colour 
of  objects,  and  way  of  illuminating  them — Disposition  and  pre- 
paration of  the  dark  field — Choice  of  the  object-glass — Focussing 
— How  to  take  the  photographs. 

Chronophotographic  Apparatus. — An  ordinary  photo- 
graphic camera  can  be  used  in  chronophotography, 
provided  that  it  is  furnished  with  a  diaphragm  which 
gives  very  short  periods  of  exposure  at  regular  in- 
tervals of  time.  For  this  purpose  the  simplest  arrange- 
ment, and  the  one  we  originally  employed,  is  a  disc 
which  is  provided  with  small  foramina,  and  which 
revolves  in  a  slot  cut  in  the  mounting  of  the  objective. 
The  disc  is  made  to  revolve  by  a  system  of  pulleys 
and  a  continuous  chain  worked  by  clockwork  and 
controlled  by  a  good  regulator.  But  there  is  a  diffi- 
culty in  combining  a  clockwork  motor  and  a  photo- 
graphic camera,  as  well  as  in  changing  the  disc 
from  time  to  time,  as  the  rate  and  frequency  of  the 
exposures  may  require,  and  this  has  induced  us  to 
abandon  so  clumsy  an  apparatus.  We  determined  to 
construct  a  special  instrument  at  once  portable  and 
capable  of  being  regulated  as  desired.  Such  an  ar- 
rangement is  the   more  necessary  because   there  are 


68 


MOVEMENT 


certain  movements  which  cannot  be  chronophoto- 
graphed  on  a  fixed  plate,  and  which  must  be  repre- 
sented as  a  series  on  a  long  photographic  film,  which 
can  be  unrolled  at  the  back  of  the  camera. 

The  chronophotographic  camera,  as  shown  in  Fig. 
45,  meets  all  the  above  requirements  ;  but,  for  the 
present,  we  must  be  content  to  describe  only  those 
parts  which  are  necessary  for  taking  photographs  on 
fixed  plates.  The  apparatus  consists  of  two  halves 
united  by  bellows.     The  hinder  part  slides  on  a  rail 


Fig.  45.— Arrangement  of  an  apparatus  adapted  for  all  the  purposes  of  chrono- 
photograpby  (scale  -j^). 


by  means  of  a  screw-rack  for  convenience  in  focussing, 
and  into  this  part  the  dark  slides  are  introduced. 
The  objective  is  contained  in  a  box  (Fig.  46)  which 
is  cleft  beneath,  and  accurately  fitted  so  as  to  slide 
into  the  front  part  of  the  apparatus.  The  cleft  under 
the  box  is  continued  into  the  mounting  of  the  objec- 
tive, and  thus  divides  the  object-glass  perpendicularly 
to  its  principal  optical  axis,  and  allows  room  for  the 
fenestrated  diaphragms.  The  latter  by  their  revolu- 
tions regulate  the  intermittent  exposures.  One  end  of 
the  bellows  fits  into  the  box  containing  the  objective, 
while  the  other,  attached    to  the   hinder  part,  com- 


DESCRIPTION   OF  THE   APPARATUS  69 

municates  by  means  of  a  large  opening  with  the  frame, 


Fig.  46.— Objective  mounted  in  a  sliding  box.     Below  can  be  seen  the  opening  for  the 
passage  of  the  circular  diaphragms. 

which  contains  both  the  ground-glass  plate  (Fig.  47) 
and  the  negative  (Fig.  50).    The  only  parts  which  call 


Fig.  47.— Frame  with  ground  glass  for  focussing  in  chronophotography  on  fix<d 
plates. 

for  special  description  are  the  circular  diaphragms,  and 
the  shaft  which  serves  to  communicate  movement  to 


70 


MOVEMENT 


them.  These  diaphragms  rotate  in  opposite  directions, 
and  as  two  foramina  pass  each  other  an  exposure 
occurs,  and  the  plate  is  illuminated.  By  this  arrange- 
ment we  can  employ  discs  of  small  size,  and  conse- 
quently greatly  reduce  the  total  dimensions  of  the 
apparatus.  In  fact,  the  dimensions  need  not  exceed 
the  size  of  an  ordinary  (24  X  30)  camera.  The  shaft, 
which  determines  the  revolution  of  the  diaphragms, 
receives  its  own  motion  from  wheels,  which  are  worked 


Fig.  48. — "Park  slide  for  negative. 

by  a  crank.  At  present,  however,  we  have  no  space 
for  a  detailed  description. 

Now,  in  focussing,  the  position  of  the  slide  must 
vary  considerably,  and  the  two  parts  of  the  apparatus 
must  be  more  or  less  separated  from  one  another. 
The  shaft  must  therefore  be  able  to  accommodate 
itself  to  these  changes  in  distance,  and  for  this  reason 
is  composed  of  square  tubes,  which  slide  one  within 
the  other  with  what  is  technically  called  a  telescopic 
action. 

Erection  of  a  Dark  Background  for  Chronophoto- 
graphy. — The    principles    of    chronophotography    on 


DESCRIPTION   OF  THE   APPARATUS  71 

fixed  plates  demand  that  the  objects,  of  which  the 
movements  are  to  be  studied,  should  be  the  only  ones 
to  appear  on  the  sensitized  plate,  and  that  the  back- 
ground should  not  throw  a  single  ray  of  light  into 
the  apparatus. 

A  black  velvet  curtain  may  be  used  for  this  purpose, 
provided  that  the  sun  does  not  shine  directly  upon  it, 
for  all  substances,  however  dark  their  colour,  reflect  a 
certain  amount  of  light  when  strongly  illuminated. 

Chevreul  pointed  out  that  the  only  means  of  obtain- 
ing absolute  darkness  was  to  blacken  the  inside  of  a 
box,  and  make  a  hole  in  one  of  its  sides.  By  the  side 
of  this  dark  hole  all  black  material  illuminated  by  the 
sun  appears  to  be  coloured.  The  nearest  approach  we 
have  been  able  to  make  to  these  ideal  conditions  of 
Chevreul  was  by  constructing  a  dark  and  capacious 
shed  (Fig.  49)  at  the  Physiological  Station,*  the  in- 
terior of  which  has  been  painted  black,  and  by  hanging 
a  black  velvet  curtain  at  the  back.  The  opening  of  the 
shed  is  eleven  metres  long  by  four  in  height.  This 
opening  is  so  situated  that  the  sun  cannot  penetrate 
into  the  interior. 


*  This  establishment,  by  permission  of  General  Assembly  and  the 
Municipal  Council  of  Paris,  was  set  up  in  Princes  Park  (Park  des 
Princes).  Here  it  is  possible  to  carry  out  certain  researches  which 
would  be  impracticable  in  laboratories  of  the  ordinary  kind.  Such  a 
field  for  research  exists  as  yet  nowhere  else.  There  is  a  long  circular 
track,  perfectly  horizontal, and  five  hundred  metres  in  circumference; 
on  this  the  ordinary  paces  of  men  and  large  animals  can  be  studied. 
By  means  of  a  dark  background,  it  is  possible  to  apply  chrono photo- 
graphy on  fixed  plates  to  the  analysis  of  long-continued  movements. 
A  background,  uniformly  illuminated,  and  of  even  surface,  offers 
facilities  for  chronophotography  on  moving  films.  Registering  dyna- 
mometers, spirometers,  pedometers,  and  various  apparatus  for  the 
measurement  of  objects  under  observation  are  devoted  to  the  study 
of  human  locomotion.  In  addition,  pneumographs,  sphygrnographs, 
and  cardiographs  enable  the  investigator  to  study  the  effect  of  athletic 
exercises  on  the  functions  of  organic  life,  ami  to  follow  step  by  step 
the  improvement  under  training.  Finally,  there  is  an  enclosure, 
where  various  kinds  of  animals  can  be  reared  in  liberty,  and  where 
their  normal  and  modified  locomotion  can  be  studied  at  pleasure. 


72 


MOVEMENT 


In  front  of  the  opening  there  is  a  track  paved  with 
blackened  wood,  along  which,  when  it  is  necessary 
to  analyze  any  particular  kind  of  movement,  the  man 
or  animal  is  made  to  walk.  Theoretically,  an  indefinite 
number  of  images  may  be  taken  in  front  of  a  dark 
background  without  any  impressions  of  outside  objects 
appearing  on  the  plate.  Practically,  when  several 
hundred  successive  images  of  a  luminous  object  have 


Fig.  49. — Arrangement  of  the  dark  background  at  the  Physiological  Station.  In  front 
of  it  there  is  a  small  chamber  running  on  rails  for  keeping  the  apparatus.  Above 
the  dark  background  a  framework  is  arranged  for  holding  the  camera  at  a  distance 
of  12  metres,  when  it  is  necessary  to  photograph  from  above. 


been  taken,  the  plate  sometimes  appears  "fogged" 
in  the  areas  which  correspond  to  the  dark  background. 
This  proves  that  a  small  quantity  of  light  emanates 
from  this  source.  The  appearance  of  "fogging" 
curtails  the  duration  of  development,  and  diminishes 
the  intensity  of  the  image.     The   slightest   reflection 


DESCRIPTION   OF   THE  APPARATUS  73 

of  light  from  the  dark  background  must  be  prevented, 
because,  however  feeble  may  be  the  light  from  this 
source,  since  it  affects  the  sensitized  plate  every  time 
the  objective  is  uncovered,  the  ultimate  sum  of  these 
insignificant  effects  will  finally  become  appreciable. 

One  of  the  important  factors  in  obtaining  a  good 
negative  is  a  pure  atmosphere.  Particles  of  (lust 
floating  in  the  air,  when  illuminated  by  the  sun,  form 
a  sort  of  luminous  haze,  which  interferes  with  the 
clearness  of  the  photographic  field.  The  effect  is  very 
n  diceable  when  a  horse  at  a  quick  pace  passes  along 
the  track  which  stretches  in  front  of  the  background. 
The  track  should  therefore  be  kept  moist,  the  soil 
in  the  neighbourhood  should  be  turfed,  and  the  inside 
of  the  shed  kept  scrupulously  clean.  It  often  happens, 
however,  that  the  rays  of  the  sun,  although  they  do 
not  penetrate  directly  into  the  interior  of  the  shed, 
nevertheless  impinge  on  the  ground  which  surrounds 
the  entrance,  and  thus  become  reflected  on  to  the  velvet 
curtain;  the  darkness  of  the  photographic  field  is  in 
consequence  considerably  reduced.  Even  if  the  ground 
of  the  shed  is  composed  of  asphalte,  it  is  as  well  to 
stretch  a  strip  of  velvet  over  those  portions  of  it  which 
are  directly  illuminated  by  the  sun.* 

In  any  case,  the  chances  of  light  being  reflected  are 
minimized  by  reducing  the  opening  of  the  shed  to  the 
smallest  possible  dimensions.  It  seldom  happens  that 
the  range  of  movement  under  observation  equals  the 
whole  length  of  the  shed,  which  measures  eleven  metres 
in  this  dimension.  CKten,  too,  it  is  unnecessary  to  utilize 
the  entire  height  of  the  opening,  which  measures  four 
metres.     This  can  be  reduced  by  means  of  blinds  and 

*  An  arrangement  which  would  be  perfect,  but  of  which  the  resources 
of  the  Physiological  Station  do  not  admit,  would  be  to  lower  the  level 
of  the  ground  inside  the  shed,  so  as  to  make  it  impossible  for  sunlight 
to  reach  it. 


74  MOVEMENT 

black  curtains  to  the  smallest  dimensions,  thus  augment- 
ing the  darkness. 

The  majority  of  experiments  do  not  require  such 
large  backgrounds,  and  can  be  carried  out  quite  easily 
under  the  best  conditions. 

A  square  box  of  0*50  metre  side,  lined  inside  with 
black  velvet,  makes  an  excellent  background,  especially 
when  the  opening  in  the  box  is  limited  in  size.  In  this 
way  photographs  can  be  taken  of  the  movements  of 
small  animals,  and,  generally  speaking,  of  all  small 
objects.  The  photographs  in  Chapter  II.  were  taken 
in  front  of  a  box  of  this  kind.  They  show  the  figures 
described  in  space  by  a  white  thread  moving  in  all 
three  directions. 

Dark  Background  for  photographing  Objects  in 
Water. — For  the  study  of  the  locomotion  of  fish,  and 
of  other  movements  taking  place  under  water,  the 
objects  to  be  photographed  must  be  themselves  brightly 
illuminated,  while  their  surroundings  are  in  total  dark- 
ness. For  this  purpose  a  rectangular  tank  with  glass 
sides  is  placed  in  front  of  a  dark  background;  the 
bottom  of  the  tank  is  similarly  made  of  glass,  and 
through  it  the  sunlight  is  allowed  to  enter  after  being 
reflected  from  a  mirror  set  at  an  angle  on  the  ground. 
This  arrangement  is  shown  in  Fig.  50.  Here  it  will 
be  noticed  that  the  glass  tank  forms  part  of  an  elliptical 
canal,  so  that  the  animals  can  move  round  and  round, 
like  horses  at  a  circus.  The  canal  is  three-parts  filled 
with  water,  and  the  transparent  part  is  illuminated  by 
means  of  an  inclined  mirror,  which  receives  the  sun's 
rays  direct,  The  canal,  mounted  on  a  high  table,  is 
furnished  with  handles,  so  that  it  can  be  easily  moved 
from  place  to  place.  It  is  set  out  in  front  of  an  open 
window,  through  which  the  sunlight  can  fall  upon  the 
inclined  mirror.  The  apparatus  is  variously  disposed 
according  to  the  time  of  day,  and  the  inclination  of  the 


DESCRIPTION   OF   THE   APPARATUS 


75 


mirror  so  set  that  it  reflects  the  sunlight  vertically 
upwards  through  the  tank.  Thus  illuminated,  all 
objects  floating  in  the  water  appear  bright,  but  the 
water  itself,  if  quite  clear,  is  perfectly  invisible.  It 
only  now  remains  to  form  a  dark  background  by 
placing  a  black  velvet  curtain  behind  the  transparent 
portion,  and  to  prevent  the  entrance  of  any  outside 
light.     This  is  done  by  means  of  a  light  rectangular 


Fig.  50. — Dark  background  for  the  study  of  movements  occurring  in  liquids. 


framework,  pyramidal  in  form,  and  covered  with  a 
black  material.  The  base  of  the  frame  envelopes  the 
glass  tank,  and  the  other  end  receives  the  object-glass. 
Ail  opening  made  near  the  top  allows  the  experimenter 
to  watch  what  is  going  on  in  the  water,  and  to  seize  an 
opportune  moment  for  taking  the  photograph  (Fig.  51). 
Photography  of  Light  Objects  in  Darkness  or  in  a  Red 
Light. — Xo  dark  background  is  needed  at  night-time, 


76 


MOVEMENT 


DESCRIPTION   OF   THE   APPARATUS  ll 

or  in  a  place  illuminate  1  by  red  light,  provided  that 
the  object  to  be  photographed  is  itself  a  luminous 
body,  such,  for  instance,  as  an  incandescent  lamp ;  the 
latter  gives  excellent  results. 

L.  Soret  was  the  first  to  make  use  of  this  arrange- 
ment. At  night,  on  the  stage  of  a  theatre,  lighted 
only  by  a  few  red  lanterns,  he  studied  the  movements 
of  dancers,  by  fastening  little  incandescent  lamps  to 
their  heads  and  feet.    In  this  way  Soret  obtained  some 


Fk;.  52.— Arrangement  employed  by  Messrs.  Demeny  and  Quenu  for  studying  (by 
means  of  chronophutograpny)  aunorma.ities  iu  walking. 

very  curious  trajectories,  in  which  the  curves  obtained 
showed  a  beautiful  and  regular  interlacement. 

Messrs.  Demeny  and  Quenu  similarly  made  use  of 
incandescent  lamps  in  analyzing,  by  means  of  chrono- 
photography,  the  characteristic  gaits  of  patients 
afflicted  with  various  kinds  of  lameness. 

A  room  in  a  hospital  was  provided  with  red  windows 

(Fig.  52),  a  track  was  marked  out  on  the  floor  for  the 

patient  to  walk  on,  and  the  apparatus  was  placed  at 

a  suitable  distance.     Incandescent   lamps  were  fixe  1 

7 


78  MOVEMENT 

to  the  joints  of  the  legs,  to  one  of  the  shoulders,  and 
to  the  head  of  the  subject.  These  lamps  were  con- 
nected with  the  battery  by  means  of  a  carriage,  which 
ran  along  wire  rails,  and  accommodated  itself  to  the 
various  movements.  The  negative  obtained  consisted 
of  a  series  of  bright  spots  corresponding  to  the  succes- 
sive positions  of  the  different  lamps.  By  connecting 
the  points  by  straight  lines  the  geometrical  chrono- 
photograph  of  the  gait  was  obtained.* 

The  combined  use  of  red  illumination  and  the 
electric  light  has  infinite  variations.  For  instance, 
if  one  arranges  a  powerful  electric  search-light  so  that 
the  beams  are  directed  across  a  room  illuminated  by 
red  light,  only  the  objects  shown  up  by  the  electric 
light  will  produce  a  reaction  on  the  photographic 
plate. 

Colour  of  Objects  and  Way  of  Illuminating  them. — 
When  the  objects  under  observation  are  white,  or  of 
some  colour  that  can  be  photographed,  strong  illumi- 
nation is  all  that  is  necessary  for  obtaining  good 
results,  because,  if  the  background  against  which  they 
are  projected  is  quite  dark,  by  slightly  prolonging  the 
process  of  development  the  images  are  made  to  stand 
out'  quite  clearly.  When,  however,  the  colour  of  the 
objects  is  difficult  or  impossible  to  photograph,  it  is 
necessary  to  colour  them  artificially. 

*  As  it  would  be  very  difficult  in  this  long  succession  of  points  to 
recognize  those  siniulta  ieously  formed,  the  following  arrangement 
was  designed:  The  diaphragm  contained  live  fenestrations,  and  con- 
sequently produced  five  images  for  every  complete  revolution.  Now, 
one  of  these  fenestrations  was  made  larger  than  the  rest,  and  con- 
sequently the  particular  image  produced  by  it  was  of  greater  intensity 
than  the"  others  on  the  plate,  owing  to  the  longer  exposure.  In  such 
a  negative  one  can  see  that  in  each  series  of  spots  every  fifth  spot  is 
more  accentuated  than  the  intermediate  ones.  These  are  the  main 
points  which  must  be  connected  by  straight  lines,  so  as  to  represent  in 
the  diagram  the  axial  position  of  the  limbs  at  successive  moments. 
As  for  the  little  intermediate  points,  they  are  not  without  their  use, 
as  by  their  degree  of  separation  one  can  measure  the  rapidity  of 
movement  of  the  vaiious  joints. 


DESCRIPTION   OF   THE   APPARATUS 


7S) 


In  our  attempts  to  represent,  by  ehronophotographic 
means,  the  various  changes  in  shape  and  appearance  of 
an  animal's  heart,  as  occurring  in  the  auricles  and 
ventricles,  we  met  this  difficulty  in  its  extreme  form, 
since  the  red  colour  of  the  muscles  and  of  the  blood 
made  no  impression  on  the  photographic  plate. 


Head 

•  •  •     v...-  •     •  •  • «■;"•  • 

Shoulder 

mmmjr V--" 

Hip 

'•••..      .  .•• " 
••• 

Knee 

// 

WW 

(■■■■■(■■■  (■■{■{({■■■■(■  ■  ■ 

Ankle 

•    •                      * 

-A 

11  \  If.. . 

<- 

Direction  of progress ion. 

Fig.  53.— Extent  of  the  movements  of  tho  le^-s  obtained  by  Messrs.  Demeny  and 
Quenu  iu  a  dark  iooui. 

By  painting  the  surface  of  the  heart  with  a  solution 
of  Chinese  white  we  have  found  it  possible  to  take  a 
photograph  of  it,  and  we  have  obtained  excellent 
results  with  very  short  exposures.  We  need  say  but 
little  about  the  best  conditions  for  illuminating:  the 
contour   of    objects.      In   this    respect   photographers 


80  MOVEMENT 

have  acquired  such  skill  that  we  can  do  no  better  than 
borrow  their  methods. 

Generally  speaking,  objects  should  be  directly 
illuminated,  but  the  dark  background  often  makes 
lateral  illumination  necessary.  When  this  latter  means 
is  employed,  the  contour  of  certain  parts  of  the  object 
may  be  very  well  defined,  but  others  may  be  too  much 
in  the  shade.  This  can  be  rectified  by  employing 
reflectors  properly  inclined.  To  sum  up,  the  problem 
of  illumination  must  be  solved  in  a  variety  of  ways, 
but  it  is  chiefly  of  importance  in  those  rarer  cases,  in 
which  artistic  effects  are  the  chief  aim. 

Disposition  and  Preparation  of  the  Dark  Field. — The 
breadth  which  one  must  give  to  the  background 
depends  upon  the  extent  of  the  movement,  the  various 
phases  of  which  we  want  to  follow.  The  opening  must 
correspond  to  the  amplitude  of  the  movement  in  such 
a  way  that  the  least  possible  amount  of  light  may 
enter  the  box.  In  the  same  plane  as  that  on  which 
the  movement  is  to  take  place,  a  metre  scale  must  be 
fixed,  and,  if  there  is  room,  the  chronometric  dial 
also. 

Lastly,  the  photographic  apparatus  must  be  placed 
just  far  enough  off  for  the  sensitized  surface  to 
correspond  to  the  limits  of  the  background.  But  to 
regulate  this,  the  limits  of  the  background  must  be 
visible  on  the  ground-glass  plate,  and  so  they  should 
be  indicated  by  placing  on  them  bright-coloured  strips, 
or  other  striking  objects. 

Choice  of  the  Objective. — When  the  observed  move- 
ment is  strictly  confined  to  one  plane,  any  sort  of 
objective  can  be  employed,  but  it  must  be  placed  at 
such  a  distance  that  the  image  on  the  ground-glass 
plate  assumes  the  proportions  required.  In  this  case 
it  is  better  to  use  an  objective  of  short  focal  length, 
since    it   admits   a  larger   quantity    of  light.     Under 


DESCRIPTION    OF   THE   APPARATUS 


other  conditions,  the  use  of  objectives  of  short  focal 
length  is  less  convenient. 

If  the  object  to  be  photographed  has  any  depth,  it 
will  appear  at  different  points  of  its  course  in  different 
perspectives,  that  is  to  say,  when  the  observer  is  only  a 
short  distance  off.     But  this  difference  in  perspective 


Fig.  54.— Chancres  which  occur  in  the  perspective  oT  a  moving  ar.imnl  ac  orJing  to 
the  distance  off  at  which  the  photographic  apparatus  is  placed. 

becomes  less  as  the  observer  moves  further  away  from 
the  object.  To  take  an  example  :  Suppose  a  bird  flies 
in  front  of  a  camera,  and  that  we  observe  its  positions, 
when  it  is  to  the  left  of  the  camera,  when  it  is  exactly 
opposite,  and  when  it  is  to  right  (Fig.  54).  In  the 
first  case  the  bird  will  be  seen  from  the  front,  in  the 


82  MOVEMENT 

second  exactly  from  the  side,  and  in  the  third  from 
behind.  These  differences  in  perspective  are  less 
appreciable  if  the  apparatus  is  removed  further  off, 
and  the  respective  images  become  more  easy  to  com- 
pare and  to  measure.  But  by  moving  the  camera 
further  away  the  images  become  smaller,  and  hence  it 
is  necessary  to  use  an  objective  of  greater  focal  length 
in  order  to  obtain  large  enough  images.  We  need 
say  no  more  on  this  subject,  since  text-books  on 
photography  give  most  exact  directions. 

Focussing. — The  object  is  brought  into  focus  on 
the  ground-glass  plate  in  the  slide  (Fig.  47).  The 
apertures  of  the  two  diaphragms  must  be  made  to 
coincide  by  turning  their  axes  with  the  hand,  and 
the  image  is  seen  through  an  opening  situated  at  the 
back  of  the  apparatus  above  the  crank.* 

How  to  take  the  Photograph. — Just  as  the  aperture 
of  the  box  is  kept  within  strictly  necessary  limits,  so 
too  is  the  length  of  the  exposure  reduced  as  much  as 
possible.  If  the  sensitized  plate  be  unnecessarily 
exposed  before  or  after  the  end  of  the  phenomenon, 
the  intermittent  exposure  of  the  objective  will  allow 
access  to  the  plate  of  small  quantities  of  light,  which 
tend  to  cause  "fogging."  This  inconvenience  can  be 
avoided  by  placing  in  front  of  the  objective  a  special 
diaphragm,  of  the  kind  which  is  worked  by  pressing 
an  indiarubber  ball  with  the  hand.  This  anterior 
diaphragm,  when  shut,  makes  it  possible  to  open  the 
shutter  of  the  dark  slide,  to  place  the  apparatus  in 
order,  and  prepare  for  the  experiment,  the  sensitized 
plate  being  meanwhile  in  darkness. 

At  the  moment  the  phenomenon   commences,  the 


*  This  portion  of  the  posterior  part  of  the  apparatus  contains  a 
special  chamber  adapted  for  photographing  upon  a  moving  film,  which 
will  be  mentioned  later.  It  is  through  this  chamber  that  the  image 
can  be  seen  upon  the  ground-glass  plate. 


DESCRIPTION   OF  THE   APPARATUS  83 

indiarubber  ball  is  pressed,  the  anterior  diaphragm 
opens,  and  the  process  begins.  As  soon  as  the  phe- 
nomenon is  over,  the  anterior  diaphragm  is  again  shut, 
and  there  is  time  to  close  the  dark  slide  without 
any  risk  of  the  plate  being  exposed  to  detrimental 
illumination. 


CHAPTER  VI 

APPLICATIONS   OF   CHRONOPIIOTOGRAPEIY   TO 
MECHANICS 

Summary. — Bodies  falling  in  air— Ballistic  experiments— The  resist- 
ance of  the  air  to  surfaces  variously  inclined — Applications  of 
chronophotography  to  hydrodynamics— Fluid  veins ;  changes  in 
shape  of  fluid  waves:  intrinsic  movements  of  fluid  waves — 
Currents  and  eddies— Influence  of  the  shape  of  bodies  placed 
in  currents— Oscillations  and  vibrations— Rolling  of  ships- 
Vibrations  of  metal  bridges. 

Bodies  falling  in  Air. — To  determine  the  movement 
of  a  falling  body  is  one  of  the  most  difficult  problems 
in  dynamics.  It  may  be  said  that  Galileo's  classical 
experiment  was  the  origin  of  all  experimental  mechanics, 
for  it  taught  us  that  a  force  could  be  measured  by  the 
motion  it  imparted  to  a  material  body. 

Motion  which  is  of  uniform  acceleration  implies  the 
absence  of  resistance;  but  when  a  body  falls  through 
the  air,  the  resistance  of  the  latter  modifies  the  law  of 
motion  :  it  increases  as  the  square  of  the  velocity,  and 
finally  becomes  equal  to  the  force  of  gravity  itself. 
At  that  moment  the  fall  becomes  uniform,  that  is 
to  say,  the  resistance  of  the  air  is  equal  to  the  weight 
of  the  body. 

Chronophotography  would  be  a  quick  and  easy 
method  of  measuring  the  resistance  offered  by  the  air 
to  bodies  of  various  forms,  and  moving  with  various 
degrees   of   velocity ;    but   experiments   of   this   kind 


APPLICATIONS   TO   MECHANICS  85 

would  have  to  be  performed  in  a  closed  space  protected 
from  every  current  of  air.  If  during  the  night-time 
a  vertical  beam  from  an  electric  lantern  were  allowed 
to  illuminate  the  under  surface  of  various-shaped 
bodies  as  they  fell  through  such  a  space,  chrono- 
photographic  images  representing  the  various  stages 
of  the  fall  could  be  taken  on  a  plate  at  successive 
intervals  of  time.* 

But  in  the  open  air  the  least  breath  of  wind  disturbs 
the  progress  of  the  moving  body,  and  if  the  fall  is  only 
a  short  one  the  resistance  of  the  air  has  not  time 
to  make  the  velocity  uniform,  and  more  especially  is 
this  the  case  if  the  object  is  a  very  light  one.  In  the 
experiment  referred  to  on  page  53,  an  indiarubber  ball 
of  30  grammes  weight  and  11  centimetres  in  diameter 
was  the  object  which  was  allowed  to  fall.  After  a 
descent  of  two  metres  the  diminution  in  acceleration 
hardly  manifested  itself.  But  this  diminution  would 
have  been  very  obvious  in  the  case  of  a  small  and  light 
air-ball. 


*  The  Machinery  Hall  at  the  Paris  Exhibition  of  1889  would  have 
lent  itself  admirably  to  experiments  of  this  kind.  The  objects  might 
have  been  allowed  to  fall  from  the  dome  of  this  immense  building 
into  a  beam  of  light,  and  side  by  side  with  this  beam  a  chain  of 
incandescent  lamps  would  have  done  excellently  as  a  scale  of 
distance ;  and,  further,  a  chronometric  dial  with  a  bright  needle 
might  have  s*rved  to  register  the  time.  Experiments  carried  out  in 
this  manner  would  have  been  very  interesting  from  the  point  of  view 
of  aarial  locomotion — they  would  have  controlled  and  amplified  the 
beautiful  researches  which  are  now  being  conducted  by  our  colleague 
and  friend  Cailletet  and  by  M.  Colardeau  at  the  Eift'el  Tower.  One 
could  calculate  the  resistance  of  the  air  for  any  particular  velocity  by 
allowing  an  object  to  fall  until,  as  shown  on  the  photographic  plate, 
the  fall  became  uniform,  because  then  the  resistance  of  the  air  would 
equal  the  weight  of  the  falling  object. 

Now,  in  a  series  of  experiments,  by  letting  the  same  object  fall 
through  the  air,  weighted  with  ever-increasing  ballast,  so  that  the 
weight  increased  as  the  following  progression — 1,  2,  3,  etc.,  it  could  be 
seen  at  what  velocity  the  fall  became  uniform.  Since  the  resistance 
of  the  air  is  always  equal  to  the  weight,  one  could  thus  calculate  for 
an  object  of  any  particular  shape  the  law  of  aerial  resistance  for 
different  degrees  of  velocity. 


86  MOVEMENT 

Ballistic  Experiments. — Chronophotography  can  re- 
cord the  path  taken  by  projectiles  which  travel  slowly, 
and  can  show  that  the  behaviour  of  such  bodies  is  in 


r'lG.  55. — The  successive  positions  of  a  projectile  in  respect  to  two  axes,  one  vertical, 
the  other  horizontal. 

accordance  with  the  shape  and  the  character  of  the 
propelling  force.  When  a  round  projectile  is  thrown 
in  a  horizontal  direction,  the  course  taken  is  obviously 
parabolic ;  it  is,  however,  affected  by  the  resistance  of 
the  air,  as  will  soon  be  shown.     If  the  projectile  de- 


Fig.  56.— Stick  thrown  horizontally  with  a  rotatory  movement  in  a  vertical  plane. 

parts  from  the  circular  form ;  if,  for  instance,  it  is  a 
stick  which  is  thrown  in  a  vertical  plane  with  a  rota- 
tory motion,  the  images  of  the  stick  will  be  found  to 
lie  in  all  directions,  but  the  centre  of  gravity,  i.e.  the 
middle  of  the  stick,  will  follow  a  parabolic  course  (Fig. 
56). 


APPLICATIONS  TO  MECHANICS 


87 


In  order  that  the  phenomenon  may  appear  more 
striking,  let  us  unite  two  bodies  of  unequal  mass  by  a 
string  and  throw  them,  giving  them  a  twist  at  the  same 
time.  These  two  bodies  (Fig.  57)  will  rotate  round 
each  other  like  a  star  and  its  satellite,  but  neither  one 
nor  the  other  will  follow  a  parabolic  trajectory  ;  but 


\ 


&~*  ©- 


*~\  I  fS~* 


Fig.  57.— Movement  of  a  sy-tem  of  two  balls  bound  togetht-r  by  a  siring. 

the  centre  of  gravity  of  the  system,  which  they  together 
constitute,  will  move  exactly  in  that  path. 

Now,  in  experiments  of  this  kind,  one  can  show  how 
the  resistance  of  the  air  modifies  the  movement  of  the 
object.  Let  us  examine,  for  instance,  the  trajectory  of 
a  round  projectile,  which  is  thrown  in  a  horizontal 
direction.     Let  us  construct  a  diagram  of  this  move- 


M 

L+~ 

— ■ 

— 

-fi 

h. 

— 1 

1 — T3- 

t* 

-~^a 

-Q 

-     1  0 

0 

Tq 

-- 

..._ 

7±=> 

-f- 

- 

_. — . 

^ 

Fig.  5S.— Trajectory  of  a  projectile  in  respect  to  two  axes  (negative  image). 

ment  (Fig.  58),  and  let  us  find  the  relationship  which 
each  position  of  the  object  bears  to  two  axes  at  right 
angles  to  one  another.  If  the  resistance  of  the  air  does 
not  interfere  with  the  horizontal  movement  forward 
the  latter  should  be  uniformly  maintained.  Xow,  if 
the  last  section  in  the  horizontal  direction  be  measured 


88  MOVEMENT 

with  compasses,  and  compared  with  the  earlier  ones,  an 
appreciable  remission  in  velocity  will  be  noticed.  In 
the  same  way,  if  the  rate  of  fall  be  measured,  its  degree 
of  acceleration  will  be  found  to  have  diminished  under 
the  influences  of  aerial  resistance.  We  have  even 
noticed  in  another  experiment  that  if  an  object  is 
allowed  to  fall  vertically  and  then  thrown  in  a  hori- 
zontal direction  from  the  same  altitude,  the  duration  of 
the  vertical  fall  is  not  the  same  in  the  two  cases.  But 
in  the  second  the  resistance  of  the  air  has  a  greater 
retarding  effect. 

This  experimental  result  struck  Captain  Uchard, 
who  was  present  at  the  Physiological  Station  when  the 
experiment  was  tried.  Applying  this  know  ledge,  which 
he  believed  to  be  new,  to  the  question  of  the  motion 
of  artillery  projectiles,  he  found  by  calculation  that 
the  resistance  offered  by  the  air  to  their  descent  was 
quite  different,  according  as  they  were  simply  let  fall 
in  a  vertical  direction,  or  were  provided  with  an  initial 
velocity.* 

Resistance  of  the  Air  to  Surfaces  variously  inclined. — 
The  constant  attempts  that  have  been  made  to  con- 
struct flying  machines  prove  that  a  complete  know- 
ledge of  the  action  of  the  air  on  inclined  planes, 
travelling  at  different  velocities,  and  at  various  angles, 
is  essential  for  success.  Clever  experimentalists  have 
succeeded  in  constructing  small,  light  machines  which, 
when  let  go  in  the  air,  glide  about,  something  after  the 
manner  of  a  soaring  bird.  The  eye  can  hardly  follow 
the  evolutions,  as  they  are  complicated,  sinuous,  and 
combined  with  an  ever-changing  inclination  of  the  axis 
of  the  system.  A  sheet  of  Bristol  board  folded  length- 
ways so  as  to  form  an  obtuse  angle,  elevated  at  the 
back  and  pointed  in  front,  was  weighted  by  means  of  a 

*  A.  Uchard,  Remarks  on  the  Laws  of  Resistance  of  the  Air.  Paris, 
Berger-Levrault.     1 1 92. 


APPLICATIONS   TO   MECHANICS  89 

steel  needle  run  through  the  longitudinal  fold.  This 
little  flying  apparatus  was  allowed  to  fall  in  a  vertical 
direction,  and  its  chronophotographic  trajectory  taken 
by  a  series  of  exposures  at  intervals  of  ^o  of  a  second. 
Fig.  59  shows  a  reverse  tracing  of  this  trajectory,  and 
must  be  read  from  the  right-hand  top  corner  down- 
wards and  towards  the  left. 

This  object  falls  at  first  vertically,  with  an  accele- 
rated velocity ;  but  it  is  soon  influenced  by  the 
rudder-like  action  of  the  curved  portion  behind,  and 
swinging  round  advances  in  a  horizontal  direction, 
then  by  degrees  it  assumes  an  upward  tendency.     At 


£& 


v 


Fig.  59.—  Chronophotographic  trajectory  of  a  flying  apparatus  describing  a  sinuous 
curve  in  the  air  (20  imag ,s  to  the  second). 

this  moment  the  speed  decreases,  its  axis  rights  itself, 
and  becomes  set  in  almost  a  vertical  position.  Next 
the  axis  approaches  to  a  horizontal  direction,  the  card 
takes  a  new  plunge  with  the  apex  directed  downwards, 
and  is  about  to  turn  upside  down  in  a  new  phase  of 
accelerated  velocity,  only  at  this  moment  the  experi- 
ment comes  to  a  sudden  termination. 

All  these  extraordinary  evolutions,  which  nowadays 
are  perfectly  familiar  to  "aviators,"  after  long  and 
patient  researches,  are  explained  by  them  as  following 
the  laws  of  Avanzini  and  Joessel,  who  showed  that  if  a 
thin  lamina  of  any  substance  were  obliquely  propelled 


00  MOVEMENT 

in  a  fluid,  the  conditions  of  its  equilibrium  were  modi- 
fied in  accordance  with  the  velocity  of  movement,  and 
in  accordance  with  the  angle  formed  between  the 
axis  of  the  lamina  and  the  direction  of  movement. 
We  cannot  now  dwell  upon  the  interpretation  of  these 
experiments,  which  ought  to  be  studied  in  a  methodical 
manner.*  It  is  only  necessary  to  indicate  how  chrono- 
photography  may  assist  in  researches  of  this  kind. 

Applications  of  Chronophotography  to  Hydrodynamics. 
— The  study  of  the  movements  of  fluids  is  very  difficult, 
and  can  only  be  accomplished  by  resorting  to  par- 
ticular methods.  Thus  Savart  illuminated  a  fluid  vein 
by  an  electric  spark,  and  observed  the  changes  in  shape 
of  the  drops  of  fluid,  as  well  as  the  distances  traversed 
by  them. 

Mr.  Boys,  applying  instantaneous  photography  to 
this  study,  obtained  excellent  results,  in  which  the 
appearance  of  the  fluid  vein  was  reproduced  by  means 
of  very  short  flashes  of  the  electric  light.  In  a  moving 
mass  of  liquid,  extremely  complex  phenomena  occur ; 
changes  of  surface  shape,  and  intrinsic  molecular  dis- 
placements. The  phenomena  can  be  represented  in 
the  form  of  chronophotographs. 

Let  us  consider  the  conditions  represented  in  Fig.  50, 
where  the  water  is  contained  in  a  tank  with  glass  sides, 
and  is  illuminated  from  below  by  sunlight  reflected  by 
a  mirror  situated  beneath  the  tank,  and  on  a  level  with 
the  ground.  If  the  water  is  perfectly  clear,  the  sun- 
light is  transmitted  through  it  without  any  escape  in 
the  direction  of  the  photographic  apparatus,  except 
from  that  part  of  the  surface  which  wets  the  side  of 
the  glass  near  the  observer.  In  this  situation  capillary 
attraction  causes  the  formation  of  a  concave  meniscus 
which  extends  all  along  the  side  of  the  glass.  The 
light  which  traverses  the  water  suffers  total  reflection 

*  See  The  Flight  of  Birds,  chap  xix.     Paris,  G.  Masson.     1890. 


APPLICATIONS   TO   MECHANICS  91 

from  the  under  surface  of  the  meniscus.  On  the 
ground  glass  of  the  camera  a  very  brilliant  and  fine 
line  may  be  seen  marking  the  level  of  the  water,  and 
which,  moving  with  it,  will  imprint  all  the  undulations 
of  the  water  on  the  photographic  negative. 

Any  internal  displacement  of  the  water  can  be  made 
visible  by  suspending  small  and  brilliant  objects  in 
the  water,  and  illuminating  them  by  the  sun's  rays. 
For  this  purpose  pieces  of  wax  and  resin  are  mixed  in 
the  required  proportion,  the  former  being  less  dense 
than  water,  and  the  latter  of  greater  specific  gravity. 
From  this  solid  material  a  number  of  small  balls  are 
moulded,  and  then  silvered  over,  in  the  same  way  that 
pills  are  silvered  by  the  chemist.  These  bright  balls 
should  be  slightly  heavier  than  water,  so  that  when 
they  are  dropped  in  it  they  slowly  sink  to  the  bottom. 
If  a  small  quantity  of  salt  water  be  afterwards  added, 
the  balls  gradually  rise  up  and  remain  in  unstable  equi- 
librium. A  paper  scale,  divided  into  centimetres,  may 
then  be  gummed  on  to  the  side  of  the  tank  above  the 
level  of  the  fluid.  This  scale,  which  will  appear  in  the 
photographs,  will  do  very  well  to  measure  the  extent 
of  the  movements  which  are  being  photographed. 
With  such  an  arrangement  a  large  number  of  experi- 
ments with  liquids  can  be  carried  out.  A  few  of  them 
are  here  represented  in  the  form  of  photographs. 

Changes  in  Shape  of  Fluid  Waves. — The  bright  line 
which  marks  the  level  of  the  fluid  shows,  on  shaking, 
variations  in  contour  such  as  those  afforded  by 
vibrating  strings.  The  ventral  segments  and  nodes 
sometimes  occupy  fixed  positions  on  the  surface  of 
the  water,  as  occurs  in  the  case  of  a  choppy  sea. 
Sometimes  they  advance  with  varying  velocity,  as  in 
rolling  breakers.  A  similar  chopping  motion  can  be 
set  up  in  the  water  by  plunging  a  solid  cylinder 
into  the  tank  at  regular  intervals,  and  thus  imparting 


92  MOVEMENT 

regular  oscillations  to  the  water.  These  rhythmic 
movements  should  be  in  that  part  of  the  tank  which 
is  furthest  removed  from  the  point  of  observation. 
The  lens  of  the  camera  should  be  left  permanently 
open,  so  that  the  bright  line  may  leave  a  track 
corresponding  to  all  the  positions  assumed,  but  with 
greatest  intensity  where  the  velocity  is  least,  that 
is  to  say,  in  the  immediate  neighbourhood  of  the 
dead  points  which  correspond  to  the  crests  and 
troughs,  for  here,  just  before  changing  its  direction, 
the  movement  is  at  a  minimum. 

*If  one  wishes  to  have  a  better  appreciation  of  the 
changes  in  velocity  during  the  different  phases  of  a 
simple  oscillation  as  represented  by  the  contour  of 
a  wave,  recourse  must  be  had  to  chronophotography. 
In  other  words,  the  admission  of  light  must  be  very 
brief,  and  the  intervals  of  time  perfectly  regular.  The 
successive  positions  of  the  level  of  the  fluid  will 
thus  be  obtained.  These  positions  will  be  represented 
as  curves,  which  will  be  further  apart  at  the  centre 
of  the  oscillations  and  closer  together  in  the  neigh- 
bourhood of  the  crests  and  troughs.  If  the  rhythm 
of  the  movement  is  changed  by  gradual  acceleration, 
another  variety  of  "  chopping  "  commences,  in  which 
the  waves  are  shorter.  In  each  case  the  profile  of 
the  wave,  as  it  passes  along  in  crests  and  troughs, 
takes  the  form  of  "  trochoids,"  a  name  invented  by 
those  interested  in  hydraulics.  Waves  moving  onward, 
billows,  and  breakers,  can  be  taken  by  chronopho- 
tography, so  as  to  show  the  speed  at  which  they 
travel,  as  well  as  the  changes  in  size  and  shape  which 
occur  in  them. 

We  took  a  photograph  of  a  wave  by  disturbing 
the  water  in  the  tank  in  the  following  way : — The 
cylinder  described  above  was  immersed  in  the  water 
just  to  the  right  of  the  transparent  part  of  the  tank 


APPLICATIONS  TO  MECHANICS  93 

in  such  a  way  that  the  cylinder  itself  did  not  appear 
in  the  photograph.  The  cylinder  was  lifted  out  and 
somewhat  sharply  plunged  again  into  the  liquid,  and 
meanwhile  a  series  of  photographs  was  taken,  repre- 
senting the  phenomenon  at  the  commencement  of  the 
operation.     At  first  there  was  a  progressive  series  of 


Fig.  60. — Chopping  waves  of  very  short  period. 

depressions  visible  along  the  surface  of  the  water, 
corresponding  to  the  moment  at  which  the  cylinder 
was  lifted  up,  and  then  a  marked  upheaval  at  the 
moment  the  cylinder  was  again  plunged  into  the 
water.  This  upheaval  travelled  along  with  diminish- 
ing amplitude,   more   or  less  interrupted   by  smaller 


Fig.  61.— Advancing  wave. 

secondary  waves,  which  advanced  with  the  primary 
one.  The  velocity  of  the  wave  could  be  estimated 
by  measuring  with  a  scale  the  distance  travelled  by 
the  summit  of  the  wave  during  the  period  of  one-tenth 
of  a  second,  which  represented  the  duration  of  the 
interval  between  each  successive  exposure.  Progres- 
sive waves  showed  incomplete  contours  when  the 
chronophotographic  method  was  adopted,  and  that 
was  because  the  hinder  surface  of  the  wave  was  the 
8 


94  MOVEMENT 

best  marked,  and  sometimes  indeed  the  only  portion 
visible.* 

Intrinsic  Movements  of  Fluid  Waves. — A  number  of 
the  bright  beads  previously  spoken  of  should  be 
thrown  into  the  tank  and  the  water  disturbed,  so  as 
to  create  either  waves  or  a  chopping  condition.  The 
trajectory   of  these   beads   in    different   parts   of  the 


Fig.  62.— Molecular  movements  within  a  simple  chopping  wave. 

waves  can  then  be  seen  in  the  photographs,  and 
consequently  the  intrinsic  or  molecular  movements 
which  occur  in  the  same  situations.  In  Fig.  62  is 
represented  the  appearance  of  a  simple  chopping  wave 
as  viewed  from  the  side.  Within  this  wave  the  mole- 
cules are  seen  oscillating,  vertically  in  the  ventral  seg- 
ments, horizontally  at  the  nodes,  and  obliquely  in  the 


Fig.  63.— Molecular  movements  within  a  series  of  chopping  waves  of  short  period. 

intermediate  positions.  To  follow  the  phases  of  this 
movement  with  greater  facility  the  waves  should  possess 
a  very  short  period,  for  there  the  molecules  may  be 
seen  describing  curves,  the  centres  of  which  are  at  the 
nodal  points.  These  facts  confirm  the  analytical 
studies  of  my  colleague  Boussinesq. 

*  It  seems  that,  owing  to  the  advance  of  the  wave,  the  meniscus 
disappears  from  the  advancing  surface  of  the  wave,  that  is  to  say, 
from  the  anterior  side. 


APPLICATIONS   TO   MECHANICS  95 

In  the  case  of  waves  which  travel  in  an  onward 
direction,  billows,  and  breakers,  the  molecular  move- 
ment is  different.  For  instance,  in  one  photograph, 
taken  after  the  sudden  immersion  of  the  cylinder,  the 
surface  molecules  are  seen  to  describe  parabolic  arcs 
in  planes  parallel  to  the  direction  taken  by  the  waves. 
The  deeper  they  are  in  the  fluid  the  less  definite  are 
the  curves  described,  and  sometimes  the  direction  of 
the  movement  is  almost  in  a  straight  line.  AVhen  the 
cylinder  is  moved  with  a  to-and-fro  movement,  the 
molecules  describe  curves  on  the  surface  of  the  fluid 
which  are  complete  rings.  In  all  such  experiments, 
the  nature  of  the  impulse  imparted  to  the  water  so 
modifies  the  character  of  the  movement  that  in  order 
to  obtain  exact  results  the  force  must  be  applied  by 
mechanical  means  instead  of  by  the  hand. 

Currents  and  Eddies.— Owing  to  the  circular  form 
of  the  tank,  it  is  possible  to  set  up  a  continuous  flow 
by  means  of  a  small  screw  immersed  in  the  water. 
The  latter,  however,  must  be  placed  out  of  sight  of 
the  observer.  The  little  bright  beads  will  participate 
in  every  movement  set  up  in  the  water. 

The  chronophotographs  will,  at  any  given  moment, 
show  the  successive  positions  of  these  shining  bodies, 
which  will  thus  serve  as  indices  of  the  path  taken 
and  of  the  velocity  acquired  by  the  various  currents 
set  up. 

An  obstacle,  consisting  of  a  sheet  of  glass,  was 
placed  in  the  current,  making  an  angle  of  about  4o° 
with  the  axis  of  the  stream.  The  glass  was  so 
arranged  that  it  touched  the  walls  of  the  tank,  and 
only  presented  its  edge  to  the  chronophotograjDhic 
objective.  A  photograph  was  taken  during  a  period 
of  three  seconds,  and  the  number  of  images  taken 
was  forty-two  to  the  second. 

On   examining   this  photograph    (Fig.   64)    it    was 


96  MOVEMENT 

discovered  that  the  various  currents  reached  the  obstacle 
in  a  more  or  less  oblique  direction,  and  that  near  the 
lower  edge  of  the  inclined  plane  the  currents  divided 
in  conformity  with  Avanzini's  theory.  At  the  back 
of  the  obstacle  the  behaviour  of  the  currents  was 
variable.    The  velocitv  of  the  molecules  in  the  different 


Fig.  64.— Changes  in  velocity  and. in  direction  which  occur  in  the  liquid  molecules  of 
a  current  which  meets  an  inclined  plane. 

parts  of  the  basin  must  be  deduced  from  the  distance 
which  separates  any  two  consecutive  images. 

The  latter  are  sometimes  fused  together  in  the  form 
of  a  continuous  trajectory,  and  thus  demonstrate  the 
sluggishness  of  the  current.  On  the  other  hand,  when 
widely  separated,  the  intervening  distances  can  be 
measured  with  a  scale.  Each  interval  represents  ^ 
of  a  second  in  time,  and  hence  the  absolute  velocity 


Fig.  65.— Effects  produced  on  a  current  by  the  immersion  of  a  solid  rectangular  box. 

of  the  stream  can  be  calculated.  It  is  equally  easy 
to  determine  the  behaviour  of  the  currents  when  they 
meet  obstacles  of  different  shape.  For  instance,  if  a 
rectangular  box  is  placed  in  the  stream  (Fig.  65),  of  the 
same  width  as  the  tank,  and  provided  with  a  glass  top 
and  bottom,  the  currents  which  meet  it  become  deflected 
from  their  course,  and   pass  with   increasing  rapidity 


APPLICATIONS  TO  MECHANICS 


97 


above  and  below.  Behind  the  obstacle  they  form  a 
number  of  eddies.  We  have  also  investigated  the 
effect  of  a  current  of  water  coming  in  contact  with 
a  body  of  pisciform  shape,  that  is  to  say,  a  solid  body, 
the  section  of  which  tapers  off  unequally  at  the  two 
extremities.* 


Fig.  66. — A  current  meeting  a  pisciform  body  at  its  thick  end. 

Experiments  of  this  kind  demonstrate  in  the  case  of 
fish  the  mechanism  of  swimming.  They  might  also  be 
useful  for  ascertaining  experimentally  the  shapes  which 
offer  least  resistance,  either  in  the  case  of  bodies  im- 
mersed in  flowing:  water  or  of  those  moving  in  still 


-A  current-  meeting  a  piscifu 


water.     The  conditions,  according  to  most  authorities, 
are  reversible. 

The  extent  to  which  eddies  occur,  or,  in  other  words, 
the  loss  of  energy,  may  be  regarded  as  a  measure  of 
the  resistance  offered  to  bodies  immersed  in  a  current. 

*  In  order  that  the  light  might  pass  up  through  such  a  body,  the 
sides  were  made  of  ebony,  and  the  superior  find  inferior  surfaces  of 
celluloid — the  contour  of  a  fish  being  preserved  throughout.  The 
light  which  pas.-ed  through  the  layers  of  celluloid  was  sufficient  to 
illuminate  the  bright  beads  which  happened  to  pass  above  the 
obstacle,  and  consequently  their  images  appeared  in  the  chrono- 
phot  graphic  negatives,  and  showed  the  paths  taken  by  the  various 
eddies. 


98  MOVEMENT 

Now,  it  can  be  seen  that  if  a  fish-shaped  body 
presents  its  thick  end  to  the  moving  water  the 
currents  track  along  the  sides,  thus  minimizing  the 
deviation  of  the  stream  (Fig.  (36) ;  but  if  the  direction 
of  the  current  is  reversed,  so  that  the  water  comes  in 
contact  with  the  pointed  end,  the  water  having  passed 
the  midship-frame,  falls  into  strong  eddies  (Fig.  67). 
This  experiment  confirms  the  opinion  already  held,  that 
a  "  piscifbrm  "  shape  is  the  most  favourable  one  that 
a  fish  could  possess,  since  the  water  offers  very  little 


Fig.  68.— Fluid  wave  surmounting  an  obstacle. 

resistance  to  sncn  forms  as  have  the  pointed  end  at 
the  posterior  extremity.* 

When  a  stream  rushes  violently  against  an  opposing 
obstacle  situated  near  the  surface,  the  water  rises  up 
in  a  heap,  and  falls  down  on  the  other  side  in  a  cascade. 
This  transient  phenomenon,  the  details  of  which  are 
not  visible  to  the  eye,  can  be  registered  in  all  its 
phases  by  chronophotography,  and  in  a  photograph 
the  successive  phases  of  the  heaping  up  of  the  water, 
as  it  Monies  in  contact  with  the  obstacle,  are  shown  by 
the  variations  in  the  water-level,  while  the  bright  beads 
serve  as  an  index  of  the  molecular  movements-  in  the 
depth  of  the  basin.  This  brief  enumeration  of  the 
applications  of  chronoJDhotography  for  the  analysis  of 

*  Chronophotography  might,  it  appears  to  us,  be  applied  to  the 
study  of  movements  in  air  when  one  wanted  to  find  the  rerjistance 
offered  by  a  body  <>f  particular  shape  to  a  current  of  greater  or  le^s 
velocity.  For  this  purpose  a  number  of  light  and  luminous  objects 
would  have  to  be  set  floating  in  the  air. 


APPLICATIONS   TO   MECHANICS 


99 


moving  fluids  will  suffice  to  demonstrate  the  resources 
of  the  method.* 

Oscillations  and  Vibrations. —  When  a  pendulum 
swings,  the  suspended  mass  is  acted  upon  by  gravity 
alternately  in  two  directions,  so  that  the  mass  alter- 
nately presents  positive  and  negative  phases  of  accelera- 
tion, dependent,  as  is  nowadays  well  known,  on  the 
continuous   action   of  gravity.     This   is  true  also  of 


Fig.   69. — Jointed  pendulum :  an  oscillation  from  right  to  left  following  on  a  halt 
oscillation  from  left  to  right. 

those  vibratory  movements  in  which  the  elastic  force 
of  a  vibrating  rod  takes  the  place  of  gravity  in  an 
oscillating  pendulum ;  but  in  some  cases  the  conditions 
of  movement  are  so  complicated  that  it  is  difficult  to 
foretell  exactly   what  the  oscillations  will  be.      This 

*  Hydraulic  engin  ers  might  also  perhaps  have  recourse  to  chrono- 
photography  when  they  want  to  prove  certain  points  in  their  theories 
concerning  waves  and  currents,  and  even  when  working  out  the  effect 
of  different  kinds  of  propellers.  This  they  might  do  b\  observing  the 
movement  transmitted  to  the  molecules  of  the  fluid  by  the  propellers. 


100  MOVEMENT 

happens  in  the  case  of  jointed  pendulums.  The  alter- 
nating swing  of  our  lower  extremities  in  running  and 
walking  is  also  of  this  nature,  for  while  the  thigh 
swings  from  the  hip  joint,  the  leg  swings  from  the 
knees,  and  the  foot  from  the  ankle.  The  movements 
which  act  and  react  upon  one  another  produce  very 
complicated  results.  Fig.  69  shows  how  chronophoto- 
graphy  can  reproduce  all  the  details. 

The  Vibration  of  Flexible  Rods. — A  distinguished 
officer  in  the  French  army  occupied  in  studying  pro- 
blems in  ballistics,  was  anxious  to  discover  whether 
the  transverse  vibrations  of  the  barrel  of  a  gun  were 


Fig.  7u.  —  Vibrations  of  an  elastic  and  wooden  rod. 

transmitted  to  the  extremity  of  the  weapon.  He  was 
under  the  impression  that,  in  vibrations  of  this  kind 
occurring  in  flexible  rods,  they  were  equally  felt  along 
the  entire  length,  and  that  even  in  the  last  segments 
the  vibrations  still  occurred  in  the  form  of  curves. 
The  experiment,  made  by  means  of  chronophotography, 
showed  that  this  was  not  the  case.  Transverse  vibra- 
tions imparted  to  a  rod  were  represented  at  the  terminal 
segments  as  rectilinear  discursions  (Fig.  70). 

The  Rolling  of  Ships.— The  so-called  "rolling"  of 
ships  presents  a  very  complicated  series  of-  problems, 
involving,  as  it  does,  not  only  the  oscillations  of  the 
boat  itself,  but  also  the  movements  imparted  to  it  by 


APPLICATIONS  TO  MECHANICS  101 

the  waves  of  a  rough  sea.  If  the  characteristic  move- 
ments of  a  boat  in  still  water  can  be  approximately 
calculated  beforehand,  those  on  a  rough  sea  can  only 
be  ascertained  by  actual  trial.  Chronophotography 
readily  lends  itself  to  researches  of  this  kind. 

Experiments  with  floating  objects,  shaped  more  or 
less  like  boats,  show  that  it  is  easy  to  discover  the 
centre  or  the  temporary  centres  of  the  rolling.  By 
placing  a  little  model  boat  in  front  of  a  dark  back- 
ground, and  by  attaching  bright  objects  to  the  mast, 
a  series  of  dotted  lines  is  obtained  by  means  of  chrono- 
photography, each  of  which  represents  one  of  the 
successive  phases  of  rolling,  and  indicates  the  position 
of  the  mast ;  but  if  these  dots  are  joined  up  so  as  to 
form  continuous  lines,  and  the  latter  are  then  produced 
until  they  intersect  below  the  level  of  the  water,  the 
exact  centre  of  oscillation  can  be  determined  for  any 
particular  moment,  provided,  of  course,  that  the  points 
of  intersection  are  accurately  obtained.  If  the  floating 
object  be  cylindrical  in  shape,  the  oscillation  takes 
place  round  the  axis  of  the  cylinder,  but  in  other  forms, 
especially  if  the  object  is  provided  with  a  keel,  the 
oscillation  takes  place  round  centres  which  are  con- 
stantly changing. 

A  celebrated  French  marine  engineer  assisted  us  in 
making  some  researches  on  the  rolling  of  ships  under 
more  practical  conditions  ;  the  experiments  were  carried 
out  with  small  models  which  represented  the  commoner 
types  of  ship. 

Similar  researches  may  be  carried  out  at  the  seaside 
by  fixing  electric  lights  to  the  mast-heads  of  boats, 
and  by  taking  photographs  of  them  during  the  dark- 
ness of  night. 

Vibrations  of  Metal  Bridges. — M.   Deslandres  *   has 

*  Deslandres,  "Action  of  Rhythmic  Shocks  upon  Metal  Bridges," 
Annales  des  Fonts  et  Chaustees,  Dec,  1892. 


102  MOVEMENT 

just  made  some  interesting  experiments  on  the  re- 
sistance of  metal  bridges,  by  means  of  stylography 
and  chronophotography.  He  recorded  vibrations  which 
proved  that  the  metal  arches  of  bridges  were  subject  to 
periodic  strains.  The  diagrams  showed  that,  if  the 
steps  of  a  horse  harnessed  to  a  carriage  harmonized  in 
rhythm  with  the  natural  vibrations  of  the  corresponding 
arches,  the  vibrations  of  the  latter  continued  to  increase 
in  amplitude,  until  the  oscillation  of  the  bridge  became 
thirteen  times  as  great  as  when  the  carriage  simply 
remained  at  rest  on  the  bridge.  We  regret  that  we 
can  do  no  more  than  simply  mention  this  remarkable 
fact. 

We  cannot  here  extend  the  applications  of  chrono- 
photography  beyond  the  study  of  mechanical  phe- 
nomena. The  reader  will  doubtless  realize  for  himself, 
from  the  instances  already  quoted,  that  such  applica- 
tions are  extremely  numerous. 


CHAPTER   VII 

CHRONOPHOTOGRAPHY   ON   MOVING   PLATES 
Principles  and  History  of  the  Method 

Summary. — Janssen's  astronomical  revolver — Muybridge's  experi- 
ments :  luminous  background — Photographic  cameras  arranged 
in  series — Control  of  the  instantaneous  shutter  by  electrical 
means  Photographic  gun — Internal  structure  of  the  instrument — 
Method  of  changing  the  photographic  plates— Principles  of 
chronophotography  on  moving  plates — Employment  of  chrono- 
photography — Necessity  for  arresting  the  progress  of  the  film  at 
the  moment  of  exposure — Moment  to  choose  for  taking  the 
photograph— Form  and  dimensions  of  the  photographs— Regula- 
tion of  the  number  and  dimensions  of  the  photographs — Repro- 
duction, enlargement,  and  reduction  of  chronophotograjihs. 

Since  the  invention  of  photography  it  has  served  as 
a  means  of  comparing  the  present  with  the  past  by  the 
help  of  authentic  reproductions. 

In  a  series  of  portraits  taken  at  different  periods  of 
life,  anybody  can  see  the  changes  wrought  by  time 
upon  the  features  of  any  particular  face ;  an  engineer 
can  survey  from  afar  the  progress  in  the  work  of 
constructing  a  building,  and  a  farmer  the  cultivation 
of  his  land. 

Mr.  Janssen  was  the  first  who,  for  the  purposes  of 
science,  thought  of  taking  by  automatic  means  a  series 
of  photographic  images  to  represent  the  successive 
phases  of  a  phenomenon.  The  honour  is  clue  to  him 
of  having  inaugurated  what  is  nowadays  called  chrono- 
photography on  a  moving  plate. 

It  was  proposed  to  take  a  series  of  photographs  of 


101  MOVEMENT 

the  planet  Venus  as  it  passed  across  the  sun's  disc, 
and  for  this  purpose  our  learned  colleague  constructed 
his  astronomical  revolver.  This  instrument  contained 
a  circular  sensitized  plate,  which  at  stated  intervals 
rotated   through    a   small    angle,   and   at    each    turn 


Fig.  71.— Facsimile  of  the  print  of  a  photographic  plate  obtained  with  the  astrono- 
mical revolver  of  the  transit  of  the  planet  Venus  across  the  sun,  Dec.  8,  1874  (by 
M.  Junssen).   , 

received  a  new  impression  on  a  fresh  portion  of  the 
plate. 

The  photograph  (Fig.  71)  which  was  obtained  by  this 
means  consisted  of  a  series  of  images  arranged  in  a 
circular  fashion ;  each  image  represented  a  new  position 


CHRONOPHOTOGKAPHY   ON  MOVING   PLATES      105 

of  the  planet  during  the  period  of  transit,  and  each  was 
separated  from  its  neighbour  by  an  interval  of  seventy 
seconds.  In  this  photograph  the  dark  silhouette  of 
the  planet  stood  out  in  strong  contrast  against  the 
white  background  formed  by  the  sun's  surface.  In 
the  first  of  the  series  the  disc  representing  the 
planet  projected  beyond  the  solar  lirubus,  but  in  the 
third  coincided  with  it.  Mr.  Janssen  made  the  further 
suggestion  of  applying  a  photographic  series  to  the 
study  of  animal  locomotion.* 

It  remained  fur  Mr.  Muybridge,  of  San  Francisco,  to 
discover,  by  means  of  a  rather  different  method  to  that 
of  Janssen,  the  analysis  of  equine  locomotion,  as  well 
as  that  of  man  and  various  animals. 

Muybridge's  Method  and  Apparatus  —  Mr.  Stanford, 
formerly  Governor  of  California,  believed  that  the 
various  positions  of  a  horse  in  executing  its  different 
paces  could  be  reproduced  by  means  of  photography, 

*  This  is  bow  our  colleague  expressed  himself  in  1878: — "The 
characteristic  of  the  revolver  is  that  it  affords  an  automatic  means  of 
taking  a  series  of  photographs  of  the  most  variable  and  rapid  pheno- 
mena in  a  sequence  as  rapid  as  may  be  desired,  and  thus  opens  up 
for  investigation  some  of  the  must  interesting  problems  in  the 
physiology  and  mechanics  of  walking,  flying,  and  various  other 
auimal  movements. 

"  A  series  of  photographs  of  any  particular  movement,  comprising 
the  entire  cycle  of  events,  would  be  a  most  valuable  means  of  elucida- 
ting the  mechanism  involved.  In  view  of  our  present  ignorance  on 
the  subject,  one  could  imagine  the  interest  of  possessing  a  series  of 
photographs  representing  tne  successive  positions  of  a  bird's  wing 
during  the  act  of  Might.  The  principal  difficulty  would  arise  from 
the  sluggishness  of  our  photographic  plates,  for  images  of  this  kind 
reqnire  the  very  shortest  exposure.  But,  doubtless,  science  will  over- 
come difficulties  of  this  kind. 

"From  another  point  of  view,  the  revolver  may  be  said  to  present 
the  reverse  picture  to  that  of  the  phenakistoscope.  31.  Plate.iu's 
phenakistoscope  is  designed  for  the  purpose  of  reproducing  the  effect 
of  a  movement,  or  of  an  action,  by  means  of  a  serit  s  of  views,  which 
represent  the  component  phases  of  the  movement  or  action.  The 
photographic  revolver  gives,  on  the  contrary,  an  analytical  repro- 
duction of  the  movement  by  representing  in  series  its  elementary 
phases." — Bulletin  de  la  Sociele  Francaise  cle  Photoqraphie,  Dec!, 
1876. 


106  MOVEMENT 

and  determined  to  have  experiments  made  on  the 
subject.  He  was  fortunate  enough  to  secure  the 
services  of  Mr.  Muybridge,  who  obtained  immense 
success  in  photographing  different  kinds  of  paces. 
A  description  has  been  given  of  these  experiments 
in  a  work  published  under  the  auspices  of  Mr.  Stanford, 
by  Dr.  Wellmann.* 

The   scene   of  the    operations   was    a   track  which 


&&«    V 


/-- 


Fig.  72. — Field  of  operations  arranged  by  Mr.  Muybridge.  On  the  left  there  is  an 
inclined  screen  which  reflects  the  sun's  rays,  and  before  which  the  horse  passes. 
On  the  right  there  is  a  series  of  photographic  cameras.  Some  other  cameras 
mounted  on  trestles  enable  the  operator  to  obtain  simultaneous  photographs  of  a 
hoise  from  variou-  points  of  view. 

passed  in  front  of  a  white  inclined  screen,  and  so 
situated  that  it  reflected  the  sunlight  in  the  direction 
of  the  photographic  apparatus  (Fig.  72).  The  screen  was 
marked  with  divisions  at  equal  distances,  which,  when 
reproduced  in  the  photograph,  served  as  a  means  of 
measuring  the  distance  traversed  by  the  horse. 

A  series  of  cameras  was  drawn  up  opposite  to  this 

*  The  Horse  in   Motion,  as  shoivn   by  Instantaneous  Photography 
London,  Turner  &  Co  ,1882. 


CHRONOPHOTOGRAPHY   ON   MOVING   PLATES      107 


108  MOVEMENT 

track,  and  electric  wires  were  stretched  across  the  path 
at  intervals.  These  latter  communicated  with  electro- 
magnets, each  of  which  held  the  shutter  of  one  of  the 
cameras  tightly  closed.  The  horse,  in  following  the 
track,  broke  these  wires  one  after  the  other,  and 
brought  about  the  instantaneous  opening  of  the  cor- 
responding shutter,  each  exposure  allowed  a  photograph 
of  the  animal,  in  one  or  other  of  its  positions,  to  appear 
on  the  plate. 

These  valuable  experiments  settled  certain  points 
with  regard  to  the  paces  of  a  horse  in  motion,  about 
which  there  had  been,  even  among  specialists,  great 
divergence  of  opinion.  Muybridge's  figures  demonstrate 
the  successive  movements  of  the  horse's  limbs,  as  well 
as  the  corresponding  position  of  its  body.  The  extent 
of  the  movement  can  be  measured  by  means  of  the 
divisions  marked  on  the  screen  (Fig.  73). 

In  an  album  kindly  presented  to  us  by  Mr.  Muy- 
bridge,  one  can  see  how  all  kinds  of  equine  paces  are 
represented,  as  well  as  those  of  the  bull,  the  stag,  the 
dog,  and  the  pig.  Instantaneous  silhouettes  of  men 
running,  jumping,  and  wrestling,  present  certain 
attitudes  which  are  very  interesting  from  the  point 
of  view  of  artistic  reproduction  of  such  movements.* 

The  Photographic  Gun. — After  the  introduction  of 
instantaneous  photography,  it  seemed  to  us  that  the 
movements  of  a  flying  bird  could  be  analyzed  by  this 
method.  We  therefore  asked  Mr.  Muybridge  to  make 
use  of  his  apparatus  to  study  the  flight  of  birds.  He 
hastened  to  accede  to  this  request,  and  when  he  came 

*  In  Mr.  Muybridge's  first  work  he  only  used  the  old-fashioned  wet- 
plate  system.  Th«  discovery  of  the  dry  gelatine  plate,  sensitized 
with  bromide  of  silver,  allowed  him  latterly  to  pursue  his  studies 
under  more  favourable  conditions,  and  to  publish  magnificent  plates 
of  animals  in  motion. 

During  late  years,  M.  Ottomar  Ansehiitz  (of  Lissa)  has  obtained, 
by  Muybridge's  method,  a  very  b  autiful  series  of  photographs  showing 
men  and  animals  in  motion. 


CHRONOPHOTOGRAPHY  ON  MOVING  PLATES   109 


Fig.  74.—  The  photographic  gun. 


110  MOVEMENT 

to  Paris,  in  August  of  1881,  he  brought  us  several 
prints  of  pigeons  photographed  in  -5l0  part  of  a  second. 
Each  of  these  photographs  represented  a  number  of 
flying  pigeons  in  different  positions,  one  with  its 
wings  raised,  another  with  them  in  front,  and  another 
with  them  depressed.  These  positions  appeared  to  us 
to  coincide  almost  exactly  with  those  which  we  had 
predicted  from  studying  the  mechanism  of  flight  by 
the  graphic  method.* 

But  beyond  the  fact  that  these  photographs  were 
not  sufficiently  clear,  they  failed  in  that  which  gave  so 
much  interest  to  those  of  the  horse  in  motion,  namely, 
the  arrangement  in  a  series  which  showed  the  successive 
attitudes  and  positions.  This  is  because  it  is  impos- 
sible  to  apply,  in  the  case  of  a  bird  in  free  flight,  the 
method  which  succeeded  so  well  in  the  case  of  a  horse, 
and  which  depended  on  the  animal  itself  opening  a 
series  of  photographic  shutters. 

We  determined  to  invent  an  apparatus  based  on  the 
same  principles  as  that  of  M.  Janssen,  but  capable  of 
giving  a  series  of  photographs  at  very  short  intervals 
of  time, —  ^2  °f  a  second  instead  of  the  70  seconds  which 
separated  the  photographs  of  the  astronomical  revolver 
— so  as  to  procure  the  successive  phases  of  the  move- 
ments of  the  wings.  This  instrument,  gun-like  in  form 
(Fig.  74),  made  it  possible  to  follow  the  flight  of  a  bird 
by  aiming  at  the  object  in  the  ordinary  manner.  The 
moment  the  trigger  was  pulled  the  sensitized  plate 
received  an  impression,  then  moved  on  only  to  receive 
another,  and  so  on,  but  always  stopping  each  time  that 
the  opening  of  the  shutter  allowed  the  light  to  fall  on 
the  plate.f 

*  "The  Graphic  Method."  p.  211. 

t  The  following  are  the  details  of  the  construction.  The  barrel  of 
the  gun  is  a  large  blackened  tube  (Fig.  75),  which  contains  an 
ordinary  photographic  lens.     At  the  hindermost  part,  mounted  firmly 


CHROXOPHOTOGRAPHY   ON  MOVING  PLATES      1 J  1 


Fig.  75. — External  appearance  of  tbe  photographic  gun 


112  MOVEMENT 

The  gelatine  plates,  sensitized  with  bromide  of  silver, 


Fig.  76.— Details  of  the  interior  of  the  photographic  gun. 

on  which  the  photographs  were  taken,  were  cut  with  a 
diamond  to  a  circular  or  octagonal  shape,  as  is  shown 

at  the  butt  end,  is  a  large  cylindrical  breech  which  contains  the  cluck- 
work  mei-hanism.  The  axis  of  the  breech  is  seen  projecting  at  B. 
When  the  trigger  is  pulled  the  wheels  begin  to  rotate  and  transmit 
the  necessary  movement  to  the  different  parts  of  the  instrument.  A 
centml  axis,  which  revolves  12  times  in  a  second,  controls  the  move- 
ment of  all  the  individual  parts  of  the  apparatus.  In  the  first  place 
(Fig.  76),  there  is  an  opaque  metal  disc  provided  with  one  small 
opening.  This  disc  constitutes  the  shutter,  and  only  allows  the  light, 
which  passes  through  the  objective,  to  gain  an  entrance  12  times  in  a 
second,  and  then  on  y  for  a  period  of  y-^  part  of  a  second.  Behind 
the  first  disc  there  is  another  provided  with  12  openings  which 
rotates  freely  on  the  same  axis  as  the  first,  and  behind  these,  again, 
there  is  room  for  the  sensitized  plate,  which  may  be  circular  or 
octagonal  in  shape.  This  fenestrated  disc  should  rotate  inter- 
mittently so  as  to  come  to  rest  12  times  in  t.  e  second  just  opposite  the 
beam  of  light  which  penetrates  the  instrument. 


CHEONOPHOTOGKAPHY  ON   MOVING   PLATES      113 

in    Fig.   78.       In    this    photograph    the    successive 
positions  of  a  flying  gull  are  shown  at  intervals  of  j\2 


Fig.  77.— Special  box  for  holding  the  photographic  plates. 

of  a  second.  These  little  images,  when  enlarged  by 
projection,  furnish  curious  details  with  respect  to  the 
position  of  the  wings,  and  the  torsion  of  the  remiges 

An  eccentric,  E,  placed  on  the  central  axis,  produces  this  intermit- 
tent rotation,  by  transmitting  a  regular  to-and-fro  movement  to  a  rod 
which  is  furnished  with  a  catch,  C.  At  each  oscillation  this  catch  is 
held  by  one  of  the  teeth  which  form  a  sort  of  circlet  round  the  fenes- 
trated disc. 

A  special  shutter,  O,  effectually  prevents  the  light  from  penetrating 
into  the  instrument  as  soon  as  all  twelve  photographs  have  been  taken. 
There  are  other  arrangements  for  preventing  the  sensitized  plate  from 
passing,  by  reason  of  its  acquired  velocity,  the  position  assigned  to  it 
by  the  catch,  and  where  it  should  remain  perfectly  still  during  the 
period  of  illumination. 

A  pressure  button,  b,  Fig.  75,  is  brought  into  close  contact  with  the 
plate,  as  soon  as  the  latter  is  introduced  into  the  gun.  Under  the 
influence  of  this  pressure  the  sensitized  p'ate  sticks  firmly  to  the 
posterior  surface  of  the  fenestrated  disc,  which  is  covered  with  india- 
rubber  to  prevent  it  slipping. 

The  object  is  brought  into  focus  by  elongating  or  shortening  the 
barrel,  and  thus  removing  or  approximating  the  lens,  and  finally  the 
process  is  corrected  by  looking  with  a  microscope  through  an  opening, 
O,  made  in  the  breech  of  the  gun,  and  observing  the  definition  on  the 
ground  glass. 


114  MOVEMENT 

by  the  resistance  of  the  air,  as  is  shown  in  Fig.  79 ; 
but  in  the  majority  of  cases  the  images  are  too  small 
to  stand  enlargement. 

To  obtain  larger  images,  certain  authors,  among 
others,  M.  Loncle  and  General  Sebert,  have  constructed 
an  apparatus  furnished  with  multiple  objectives,  the 
shutters  of  which   open  in   succession.      But   such  a 


Fig.  78. — Photograph  of  a  gull  during  flight.     Reproduction  by  means  of  Heliogravure 
of  a  cliche  obtained  by  means  of  the  photographic  gun. 

multiplication  of  objectives  is  productive  of  serious 
difficulties.  Besides  making  the  instrument  very 
costly,  especially  if  objectives  of  good  quality  are 
used,  photographs  are  produced  which,  taken  from 
different  points  of  view,  are  incapable  of  comparison. 
This  is  not  the  case  with  photographs  of  small 
dimensions  taken  at  a  short  distance.     These   cameras 


CHRONOPHOTOGRAPHY  ON  MOVING  PLATES      115 

regard,  if  one  can  use  the  expression,  the  object  from 
different  points  of  view.  Now,  these  variations  in 
perspective,  although  presenting  few  difficulties  when 
operating  from  afar  on  objects  of  large  size,  would 
make  the  study  of  small  objects  at  close  quarters  a 
matter  of  great  difficulty,*  still  less  would  they  permit 
one  to  photograph  objects  of  microscopical  size. 
For  this  reason  we  determined  to  employ  a  single 
objective. 

In  order  that  we  might  simplify  the  instrument  as 
much  as  possible,  we  united  in  a  single  apparatus  all 
the  accessories  necessary  for  chronophotography  on 
fixed  or  moving  plates,  as  well  as  for  regulating  at 
will  the  frequency  and  duration  of  the  exposures. 


Fro.  79.— Enlargement  of  one  of  the  photographs  obtained  with  the  photographic  gun. 

Principles  of  Chronophotography  on  Moving  Plates. — 
The  weak  point  of  the  photographic  gun  was  princi- 
pally that  the  images  were  taken  on  a  glass  plate,  the 
weight  of  which  was  exceedinglv  great.  The  inertia 
of  such  a  mass,  which  continually  had  to  be  set  in 
motion  and  brought  to  rest,  necessarily  limited  the 
number  of  images.  The  maximum  was  12  in  the 
second,  and  these  had  to  be  very  small,  or  else  they 
would  have  required  a  disc  of  larger  surface,  and 
consequently  of  too  large  a  mass. 

These  difficulties  may  be  overcome  by  substituting 
for  the  glass  disc,  a  continuous  film  very  slightly  coated 
with  gelatine  and  bromide  of  silver.  This  film  can  be 
made  to  pass  automatically  with  a  rectilinear  move- 
ment across  the  focus  of  the  lens,  come  to  rest  at  each 

*  See  Chap.  v.  p.  81. 


116 


MOVEMENT 


period  of  exposure,  and  again  advance  with  a  jerk.  A 
series  of  photographs  of  fair  size  can  be  taken  in  this 
way. 

The  size  we  chose  was  9  centimetres  square,  exactly 
the  right  size  to  fit  the  enlarging  camera,  and  by 
which  they  could  be  magnified  to  convenient  propor- 
tions. Now,  as  the  continuous  film  might  be  several 
metres  in  length,  the  number  of  photographs  that 
could  be  taken  was  practically  unlimited. 

Arrangement  of  the  Chronophotographic  Apparatus. — 


Fig.  80. — Internal  structure  of  the  photographic  chamber. 

The  necessary  elements  for  taking  successive  images 
on  a  continuous  film  are  united,  as  we  have  said,  in  the 
apparatus  already  known  to  the  reader.  The  back 
part  of  this  apparatus  has  a  special  compartment,  the 
photographic  chamber  (Fig.  80),  in  which  the  sensitized 
film  is  carried.  To  admit  light,  all  that  is  necessary  is 
to  substitute  for  the  frame  which  carries  the  fixed  plate 
another  frame  provided  (Fig.  81)  with  an  aperture,  the 
size  of  which  can  be  varied  at  pleasure.  This  is  the 
admission  shutter.      At  each  illumination   the   light 


CHEONOPHOTOGRAPHY  ON  MOVING   PLATES      117 

passes  through  this  aperture,  and  forms  an  image  on 
the  moving  film,  which  has  previously  been  brought 
into  focus. 

The  film  unrolls  itself  bv  a  series  of  intermittent 


Frc  81.— Admission  shutter  which  is  substituted  for  the  dark  slide  when  working 
with  a  roll  of  film.  The  size  of  the  aperture  can  be  regulated  by  the  side  scieens 
R  K,  according  to  the  dimensions  of  the  intended  image. 

movements,  by  means  of  a  special  mechanical  arrange- 
ment, which  enables  it  to  pass  from  one  bobbin  to 
another.  The  arrangement  of  these  bobbins  must 
first  occupy  our  attention,  for  the  possibility  of  loading 

H 


Ftg.  82.— Two  metal  bobbins  for  carrying  the  sensitized  film.  The  two  bobbins  are 
placed  in  different  positions  :  the  letters  H  and  B  indicate  respectively  the  upper 
and  lower  parts. 

or   unloading   in   the   light   is    dependent    on    their 
construction. 

The  bobbins  are  made  of  metal,  and  two  projecting 
plates  are  fixed  to  the  two  ends  of  a  light  cylinder. 
The  upper  of  these  plates  is  thin  and  the  lower  one 


118  MOVEMENT 

thick.  The  bobbins  rotate  on  a  vertical  pin  which 
runs  through  their  centre.  A  circle  of  little  holes 
bored  in  the  lower  plate  of  the  bobbin  forms  part 
of  the  motor  mechanism.  When  a  peg  fixed  in  a 
revolving  plate  enters  one  of  the  holes  of  the  other 
plate,  the  two  will  rotate  together,  carrying  the  bobbin 
with  them. 

One  of  these  bobbins  serves  to  store  the  sensitized 
film,  which  is  rolled  round  it,  and  which  is  finished  off 
at  the  ends  by  strips  of  opaque  paper  pointed  at  the 
extremities.  One  of  these  pointed  ends  fits  into  a  slit 
made  lengthways  in  the  bobbin,  and  the  rolling  up  can 


fT~T~:" 


Sensitized  film 


Fig.  83.— Showing  liow  the  film  is  lengthened  at  its  two  extremities  by  the  opaque 
bands  of  paper. 


thus  be  effected.  In  the  process  of  rolling,  the  strip 
of  paper  comes  first,  then  the  sensitized  film  which  is 
joined  to  it,  and  then  the  second  strip  of  paper.  An 
elastic  band  put  round  the  bobbin  keeps  the  entire  roll 
securely  fastened.  This  operation  is  executed  in  the 
dark  room,  but  as  soon  as  it  is  finished  the  charged 
bobbin  can  be  carried  into  the  light,  for  the  sensitized 
film  is  protected  by  the  coils  of  opaque  paper. 

Charging  the  Apparatus. — On  opening  the  photo- 
graphic ch amber,  two  vertical  pins  may  be  seen 
(Fig.  80) ;  that  on  the  left  receives  the  supply  bobbin, 
the  filling  of  which  has  already  been  described,  and 
that  on  the  right  is  for  the  receiving  bobbin — that  is  to 
say,  the  one  which  will  receive  and  roll  up  the  film,  or 


CHRONOPHOTOGRAPHY   ON  MOVING  PLATES      119 

as  much  of  it  as  has  been  used  in  taking  the  photo- 
graphs. That  this  may  work  properly,  the  end  of  the 
strip  of  paper  which  is  last  wound  round  the  supply 
bobbin  must  be  fixed  in  the  slit  of  the  receiving 
bobbin.  The  method  of  rolling  is  represented  in 
Fig.  84.  The  two  bobbins  being  placed  on  their 
respective  pins,  the  strip  of  paper  passes  through  a 
vertical  slit,  and  through  which  it  keeps  running, 
pulling  the  sensitized  film  after  it.  Two  pressure 
rollers  (r  r,  Fig.  80)  are  applied  to  the  surface  of  the 
bobbins  to  ensure  regularity  in  rolling  and  unrolling. 


Fig.  84. — Supply  bobbin  ready  charged.  M,  the  end  of  the  paper  which  covers  it, 
must  be  unrolled  and  wound  round  the  receiving  bobbin,  R,  in  an  opposite 
direction. 


We  shall  not  describe  the  mechanism  which  produces 
the  intermittent  movement  of  the  film.  The  new 
arrangement  which  we  have  adapted  to  the  apparatus 
for  making  the  operation  more  certain,  and  its  employ- 
ment more  easy,  differs  noticeably  from  that  which  we 
have  described  before.* 

It  would  be  better  for  the  beginner,  instead  of 
relying  on  a  written  description,  to  make  a  few 
experiments  with  a  strip  of  ordinary  paper  in  place 
of  the  sensitized  film,  and  thus  he  would  soon  acquire 
proficiency  in  filling  the  bobbins,  and  passing  them 
quickly  into  their  proper  chamber. 

*  Revue  Ge'nerale  des  Sciences,  November  15,  1891. 


120  MOVEMENT 

A  crank  placed  behind  the  chronophotographic 
apparatus  turns  all  the  wheels  of  the  instrument,  as 
well  as  the  circular  diaphragms.  A  movement,  so 
rapid  as  this  must  necessarily  be,  is  bound  to  be 
continuous,  for  it  would  be  impossible,  as  in  the  case 
of  the  photographic  gun,  to  remit  or  continue  the 
movement  of  such  heavy  bodies.  The  film  itself 
comes  to  rest  at  the  moment  of  exposure,  arrested  by 
a  special  mechanism  which  allows  it  to  continue  its 
movement  as  soon  as  the  image  has  been  taken. 

Necessity  for  arresting  the  Progress  of  the  Fi^m  at  the 
Moment  of  Exposure. — Some  people  have  thought  that, 
by  using  such  a  complicated  apparatus  as  that  which 
we  have  employed  for  arresting  the  movement  of  the 
film,  we  have  given  ourselves  unnecessary  trouble,  and 
it  has  been  said  that  for  very  short  exposures  the  move- 
ment of  the  film  might  be  neglected.  It  would  be 
easy  to  prove  by  calculation  that,  during  the  period  of 
the  exposure,  say  j^qq  part  of  a  second,  the  film 
would  move  enough  to  deprive  the  photographs  of 
that  clearness  upon  which  their  value  depends.  But 
it  is  simpler  and  perhaps  more  convincing  to  show  by 
an  experiment  that  without  these  periods  of  arrest 
good  images  are  not  to  be  obtained. 

By  alternately  suppressing  and  inducing  an  arrest 
of  the  film  at  the  moment  of  exposure,  we  obtained 
a  series  of  images  which  were  alternately  blurred  and 
distinct.  In  Fig.  85  two  such  consecutive  images  are 
shown.  The  different  degrees  of  definition  is  so 
obvious  that  it  is  useless  to  further  insist  on  the 
necessity  of  arresting  the  film  during  the  period  of 
exposure. 

The  Moment  to  choose  for  taking  the  Photograph. — 
When  the  chronophotographic  apparatus  is  pointed  at 
the  object  the  movements  of  which  are  to  be  studied, 
the  wheels  are  put   in   motion    by  turning   a   crank, 


CHRONOPHOTOGRAPHY   ON   MOVING   PLATES      121 

the  different  parts  acquire  a  uniform  speed,  but  the 
film  remains  stationary  until  the  moment  when  the 
observed  phenomenon  takes  place.  At  this  juncture 
the  operator  presses  the  trigger,  the  film  begins  to 
move,  and  the  photographs  are  taken  as  long  as  the 
pressure  is  maintained  on  the  trigger;  as  soon  as  the 
pressure  is  remitted  the  progress  of  the  film  is  arrested. 
The  employment  of  this  trigger  makes  it  possible  to 


Fig.  85  —Two  successive  photographs  taken  on  a  sensitized  film.  The  image  on  the 
left  i*  taken  without  arresting  the  onward  movement  of  the  film  at  the  moment  of 
exposure;  that  on  the  right  is  taken  with  the  film  at  rest. 

continue    taking    photographs    until    the    bobbin   is 
exhausted. 

Shape  and  Size  of  the  Photographs. — The  shape  and 
size  of  the  photographs  should  be  in  conformity  with 
the  character  of  the  subject,  so  as  to  utilize  to  the 
best  advantage  the  surface  of  the  film.  For  this 
purpose  the  opening  of  the  admission  shutter  should 
be  regulated  to  meet  the  requirements  of  the  case,  and 
the  position  of  the  apparatus  correspondingly  altered. 
Thus  the  photograph  of  a  man  in  an  upright  position 


122 


MOVEMENT 


Fig,  86.— Sword-stroUe.    The  series  must  be  read  from  below  upwards. 


CHRONOPHOTOGRAPHY   ON   MOVING  PLATES      123 

executing  movements  on  the  same  spot  should  be 
taken  on  a  surface  the  height  of  which  is  greater  than 
its  breadth;  on  the  other  hand,  two  men  occupied 
in  fencing  would  require  an  opening  the  breadth  of 
which  is  greater  than  the  height  (Fig.  86).  The 
same  is  the  case  in  taking  successive  photographs  of 
a  man  rowing.  The  background  of  the  image  should 
be  regulated  by  reducing  the  opening  of  the  admission 
shutter  to  a  greater  or  less  degree.  When  the  images 
occupy  most  space  in  the  horizontal  direction  the 
camera  should  be  turned  over  on  its  side ;  the 
successive  attitudes  should  then  be  viewed  by 
beginning  at  the  toj)  and  travelling  downwards. 

Regulation  of  the  Number  and  Size  of  the  Images. — If 
the  progress  of  the  film  is  uniform,  and  allows,  say, 
ten  large  images  to  be  taken  in  the  second,  twenty 
images  half  the  size  may,  if  necessary,  be  taken  in 
the  same  time,  or  thirty  images  a  third  of  the  size, 
and  so  on.  To  effect  this,  the  size  of  the  admission 
shutter  must  first  be  reduced  to  one-half  or  one-third 
of  its  normal  size.  It  is  important  that  the  circular 
diaphragm  should  permit  at  the  same  time  the 
exposures  to  be  twice  or  three  times  as  numerous. 
The  fenestrations  in  the  diaphragm  should,  therefore, 
have  curtains  which  can  be  drawn  aside  or  closed  as 
required.* 

Reproduction,  Enlargement,  and  Reduction  of  the 
Photographs. — The  size  which  we  have  selected  for 
chronophotographic  images  (9  x  9)  is,  as  we  said, 
precisely  that  adopted  for  the  plates  used  for  enlarging- 
cameras.  Each  photograph  can  be  thrown  on  a  screen, 
if  required   for   public   demonstration.     The   strip   of 

*  In  the  arrangement  we  previously  adopted,  the  number  of  times 
the  film  was  brought  to  a  position  of  rest  had  to  be  regulated  by 
a  very  delicate  manoeuvre ;  this  was  dispensed  with  in  the  new 
arrangement. 


124 


MOVEMENT 


CHKONOPHOTOGKAPHY  ON   MOVING   PLATES      125 

filni  itself,  or  at  least  the  series  of  positive  images 
obtained  from  it  by  superposition  on  a  similar  strip, 
can  produce  a  series  of  effects  following  one  another  in 
such  rapid  sequence  that  the  spectator  sees  the  move- 
ment reproduced  in  all  its  phases.  This  synthetical 
representation  of  movement  will  be  described  further 
on.  For  ordinary  publication  the  images  are  repr<  >duced 
by  means  of  a  special  process  called  "  simili-gravure." 
Most  of  the  figures  scattered  in  the  text  were  obtained 
by  this  process.  But  as  simili-gravure  requires  a 
special  treatment  of  dotting,  or  hatching,  to  give  the 
shapes  of  the  shadows,  it  would  be  of  no  use  for 
reproducing  very  small  photographs  of  microscopical 
objects,  nor  for  very  graduated  shading  such  as  is 
required  for  the  delineation  of  muscles.  In  these 
two  cases  we  had  recourse  to  impressions  made  with 
lithographer's  ink.  When  a  long  series  of  photo- 
graphs has  to  be  reproduced,  showing  the  successive 
phases  of  a  phenomenon,  plates  of  special  size  must  be 
used,  or  otherwise  only  a  small  number  of  images  can 
be  obtained.  If  these  photographs  are  reduced  so  as 
to  suit  the  limitations  of  a  page,  they  lose  much  of 
their  merit  and  interest.  This  occurred  in  the  case  of 
Fig.  87,  in  which  eight  reduced  images  are  represented, 
each  occupying  one-fourth  of  the  space  occupied  in 
the  original  plate. 


10 


CHAPTER  VIII 

HUMAN    MOVEMENTS 
From  the  Point  of  View  of  Kinetics 

Summary.  — Some  movements  in  man;  the  study  of  them  by  the 
graphic  method — Speed  of  different  paces  in  man  ;  relationship 
between  the  frequency  and  length  of  stride — Duration  of  tin- 
rise  and  fall  of  the  foot  in  walking  and  running — Path  described 
by  any  particular  part  of  the  body  during  different  paces; 
mechanical  means  of  recording  it — The  study  of  movements 
in  man  by  means  of  chronophotography  on  fixed  plates;  long- 
jumping;  high-jumping — Skilled  movements,  fencing,  etc. — 
Jumping   rom  a  height — The  swing  of  the  leg  in  walking. 

Sooie  Movements  in  Man. — The  ancients,  who  positively 
worshipped  physical  exercises,  only  understood  them 
from  the  point  of  view  of  practical  experience;  they 
were  entirely  ignorant  of  the  functions  of  muscles, 
but  they  knew  how  to  turn  out  a  good  runner  or 
wrestler.  Later  on,  as  anatomy  revealed  the  structure 
of  the  human  frame  and  the  muscular  system,  it  was 
the  current  belief  that  the  function  of  an  organ  was 
dependent  on  the  shape  or  form,  and  in  consequence 
a  system  of  physical  training  was  established  on 
entirely  erroneous  theories.  Doubtless  it  would  have 
been  wise  to  have  retained  the  traditions  which  were 
founded  on  practical  experience,  until  such  time  as 
Science  was  in  a  position  to  impose  really  useful 
amendments. 

It  was  not  till  the  seventeenth  century  that  Borelli 


HUMAN   MOVEMENTS  127 

threw  some  light  upon  the  mechanism  of  animal 
locomotion.* 

This  learned  Neapolitan  professor  applied  to  the 
case  of  moving  creatures  the  same  mechanical  laws 
which  had  recently  been  discovered  by  Galileo,  and 
showed  that  the  effect  of  muscular  force  made  itself 
felt  partly  on  the  mass  of  the  body,  and  partly  on 
another  mass  which  was  called  the  point  of  resistance, 
and  he  reduced  to  its  simplest  form  the  general  theory 
of  locomotion.  But,  to  impart  some  accuracy  to  the 
study  of  human  movements,  it  was  found  essential  to 
construct  instruments  to  measure  the  range,  velocity, 
and  sequence  of  the  various  phases  of  movement,  not 
only  in  walking,  but  also  in  running,  jumping,  etc. 
The  force  exercised  in  executing  these  different  move- 
ments should  also  have  been  measured;  but  the 
necessary  instruments  were  not  in  existence. 

Two  celebrated  mathematicians,  the  brothers  Weber, 
realized  the  necessity  for  accurate  measurements,  but 
inefficient  instruments  were  all  they  had  at  their 
disposal.  A  level  piece  of  ground  of  known  length,  a 
watch  provided  with  a  second's  hand,  and  a  performer 
was  all  they  had  to  work  with ;  they  could  therefore 
only  obtain  a  small  number  of  measurements  with 
regard  to  the  relationship  between  the  frequency  and 
length  of  stride,  of  the  extent  of  the  vertical  head 
displacements  and  of  the  various  inclinations  of  the 
body,  and  even  then  these  measurements  had  to  be 
corrected. 

AVith  the  assistance  of  the  graphic  method,  we  deter- 
mined to  introduce  accuracy  into  these  studies,  but  it 
was  chiefly  by  means  of  chronophotography  that  we 
arrived  at  a  scientific  interpretation  of  the  various 
bodily  movements. 

Before  giving  the  results  furnished  by  this  method, 

*  Borelli,  De  Motu  Animalium. 


128  MOVEMENT 

and  thereby  demonstrating  its  importance,  it  would 
be  as  well  to  briefly  sum  up  the  results  of  other 
methods.  Such  a  review  is  the  more  necessary, 
because  chronophotography  has  nothing  to  do  with 
other  methods,  its  application  only  becomes  of  real 
value  when  mechanical  methods  can  no  longer  be 
employed. 

Speed  of  Different  Paces  in  Man,  Relationship  between 
the  Frequency  and  Length  of  Stride. — A  man  in  walking 
or  running  covers  at  each  stride  a  certain  amount  of 
ground,  and  the  more  steps  he  takes  in  a  given  time 
the  greater  is  the  total  distance  he  covers.  Similarly, 
if  the  stride  is  increased,  but  the  number  kept  the 
same,  the  distance  will  be  proportionately  greater. 
Speed,  therefore,  depends  on  two  factors :  the  length 
and  frequency  of  the  stride.  Now,  the  brothers 
Weber  enunciated,  as  the  result  of  their  studies,  that 
the  length  of  stride  became  greater  as  the  frequency 
increased  ;  a  slow,  processional  step,  for  instance,  being 
shorter  than  one  executed  at  a  greater  rate.  If  this 
were  the  invariable  law,  the  march  of  troops  might 
be  indefinitely  accelerated  by  quickening  the  time  of 
the  drums  or  trumpets  which  regulated  the  pace.  But 
our  experiments  showed  that  this  theory  of  the  brothers 
Weber  was  only  correct  up  to  a  certain  point,  namely, 
until  the  step  was  so  quick  that  it  amounted  to  a  run, 
and  after  that  point  was  reached  the  rate  of  progression 
soon  diminished.  Our  experiments  were  made  in  the 
following  manner : — 

Being  fully  persuaded  that,  if  one  wanted  to  estimate 
exactly  the  average  length  of  stride,  it  Avas  necessary 
to  carry  out  the  experiments  on  a  long  track,  we 
laid  out  at  the  Physiological  Station  a  circular  and 
perfectly  horizontal  course,  five  hundred  metres  in  cir- 
cumference;  a  telegraph  wire  ran  all  the  way  round 
the  track,  and  the  posts  were  placed  at  intervals   of 


HUMAN   MOVEMENTS 


129 


130  MOVEMENT 

fifty  metres.  Each  post  was  provided  with  a  little 
contrivance  for  breaking  the  circuit  the  moment  the 
performer  came  abreast  of  the  post.  Within  the 
laboratory  a  recording  apparatus — "the  fixed  Olograph" 
— was  in  communication  with  the  telegraph  wires. 

In  this  apparatus  a  needle  traced  a  horizontal  line 
upon  the  paper  which  covered  a  revolving  cylinder, 
and  every  time  the  performer  broke  the  circuit,  as 
he  passed  a  post,  the  needle  was  displaced  for  a 
moment  from  its  course  and  executed  on  the  tracing 
a  rectangular  inflection.*  As  these  inflections  were 
repeated  every  time  the  performer  passed  a  post  and 
completed  a  distance  of  fifty  metres,  it  followed  that, 
at  the  end  of  a  given  time,  the  odograph  had  described 
a  zigzag  curve  which  showed  the  rate  of  progression. 

Time  is  measured  on  the  odographic  curve  by 
referring  to  the  horizontal  divisions,  which  are  marked 
along  the  axis  of  the  abscissae,  and  are  numbered  0-16, 
each  division  representing  one  minute.  The  distance 
travelled  is  measured  in  metres  along  the  axes  of 
the  ordinates.  So  that  for  every  point  of  the  curve  the 
time  occupied  and  the  space  traversed  may  be  estimated 
by  referring  to  the  intersections  of  the  vertical  and 
horizontal  lines.  The  relationship  of  these  two  values 
gives  the  actual  speed. t 

Instead  of  the  staircase  line  (a)  traced  by  the 
odograph,  it  is  better  to  draw  a  line  connecting  all  the 
angular   projections  on  the  curve ;    in  this  way  were 

obtained   the   lines   o,  b,  d, ?',  which    express   by 

their  variation  in  inclination  the  speed  of  different 
paces.  They  represent  a  uniform  rate  when  they  are 
rectilinear,  a  variable  speed  when  they  are  curved.  So 
far  we  only  know  the  rate  of  progression  with  its  two 
factors — time  occupied  and    space  traversed — at  each 

*  See,  for  details  of  the  experiment,  La  Nature,  1887 
t  See  C.  B.  de  V Academic,  November  3,  1884. 


HUMAN   MOVEMENTS 


131 


point  of  the  curve.  It  was  important  from  one  point 
of  view  to  know  the  number  of  steps  taken.  For  this 
purpose  we  placed  in  the  centre  of  the  track  a  bell 
which  rang  at  regular  intervals,  and  with  which  the 
performer  kept  time.  The  intervals  could  be  regulated 
by  means  of  a  pendulum,  the  length  of  which  could 
be  varied  at  pleasure.  It  was  situated  inside  the 
laboratory,  and  could  control  the  rate  of  ringing  for 
anything  between  40  and  120  strokes  a  minute.  The 
number  of  steps  per  minute  being  thus  known,  one 
could  substitute  in  the  odographic  tracing  the  total 
number  of  steps  taken  for  the  time  occupied,  and  by 


0      1       2       3       b       5 
Fig.  89. — Chart  of  the  fixed  odograph  to  show  paces  of  different  velocity. 

dividing  the   distance  traversed   by  that  number,  we 
could  arrive  at  the  average  length  of  stride. 

It  was  from  such  data  that  Fig.  90  was  constructed. 
This  diagram  showed  that  the  length  of  stride  increased 
as  the  step  was  quickened,  that  is  to  say,  when  the 
rate  was  between  40  and  75  per  minute.  This  was  just 
as  the  brothers  Weber  had  showed ;  but  when  the 
rate  was  quickened  beyond  that  point,  the  length  of 
stride  decreased,  and  finally  at  85  steps  per  minute 
and  onwards  the  total  rate  of  progression  began  to 
diminish.  That  is  to  say,  the  shortening  of  the 
step  became  so  pronounced  that  in  spite  of  the  increase 
in  frequency,  the  total  distance  traversed  in  a  given 


132 


MOVEMENT 


time  was  markedly  diminished.  These  experiments, 
which  for  the  most  part  were  carried  out  on  marching 
troops,  have  been  repeated  on  a  large  number  of  men 
of  various  sizes,  both  with  and  without  burdens,  and 
in  the  case  of  veterans  as  well  as  in  the  case  of  recruits. 
The  influence  of  various  inclines  on  the  length  of 


+V 

j  Length      of 

step 

tf°!-1 

""" 

**», 

VeV^l. 

1 "* 

^0  <*5  50  55  60  65  7^  75 

Fig.  90.— Curves  to  show  the  rate  and  length  of  the  stride. 


85        90S.eps 
r  minute 


stride  was  also  investigated,*  as,  too,  was  the  shape  of 
the  shoe  both  with  respect  to  the  length  of  the  sole 
and  the  height  of  the  heel.f 

All  these  experiments  on  running  and  walking  were 
carried  out  on  men,  some  of  whom  carried  weights,  while 
others    were   unburdened.      Exact   results    have    been 


*  Experiments  on  different  kinds  of  tracks  were  made  elsewhere 
than  at  the  Physiological  Station  by  a  slightly  different  method.  A 
track  of  known  length,  an  automatic  counter  of  the  number  of  steps, 
and  a  watch  with  a  second's  hand  furnished  the  necessary  appliances 

t  The  length  of  a  step  does  not  entirely  depend  on  the  degree  of 
separation  of  the  legs  :  this  would  be  the  case  if,  as  in  the  legs  of 
a  compass,  they  only  touched  the  ground  at  two  points;  but  the 
length  of  foot  must  be  takei  into  consideration  when  estimating 
the  length  of  a  step,  for  the  foot  touches  the  ground  first  with  the 
heel,  while  the  toe  is  the  last  part  to  leave  the  ground,  'lhus  in 
esti muting  the  total  length  of  the  stride,  the  length  of  the  foot  which 
is  extended  along  the  ground  must  be  added  to  it.  It  follows  then, 
that  for  lege  of  equal  length,  those  which  have  the  smallest  feet  take 
the  shortest  steps,  and,  similarly,  that  a  s!  ort  boot  will  have  the  same 
shortening  effect.  Finally,  a  high  heel,  by  curtailing  the  total  length 
of  foot  in  contact  with  the  ground,  will  also  detract  from  the  length 
of  stride. 


HUMAN  MOVEMENTS  133 

obtained  without  the  help  of  photography  ;  moreover, 
the  latter  method,  although  it  could  give  exact  details 
of  any  particular,  for  instance,  as  to  the  length  of  any 
stride  considered  by  itself,  could  not  furnish  the  re- 
quired averages. 

Mechanical  Record  of  Movements  in  Walking. — We 
saw  in  Chapter  I.  how  the  duration  and  sequence  of 
the  rise  and  fall  of  the  foot  in  walking  could  be  re- 
corded by  mechanical  means.  This  chronographic  re- 
cord was  effected  by  transmitting  through  the  medium 
of  pneumatic  tubes  the  pressure  of  the  foot  on  the 
ground  to  the  registering  tambours.  We  showed  the 
result  of  these  observations,  and  shall  now  continue 
the  investigation. 

In  ordinary  walking  on  level  ground  one  foot  leaves 
the  ground  as  the  other  reaches  it.  In  the  case  of  a 
man  who  carries  a  weight,  or  who  walks  uphill,  or 
mounts  a  staircase,  the  foot  in  contact  with  the  ground 
does  not  leave  it  until  the  other  has  been  in  contact 
with  it  for  some  time.  There  is  then  a  period,  more  or 
less  prolonged,  during  which  both  feet  simultaneously 
rest  upon  the  ground.* 

In  running,  the  body  remains  suspended  in  air  for  a 
brief  moment  between  two  successive  contacts,  and 
this  suspension  lasts  longer  as  the  speed  of  running 
increases. 

Path  described  by  any  Particular  Part  of  the  Body 
during  Different  Paces. —  So  extensive  are  the  move- 
ments in  walking,  and  even  more  so  in  running,  that 
mechanical  registration  of  these  movements  becomes 
very  difficult,  and,  further,   they  nearly  always    take 

*  By  substituting  electric  for  pneumatic  signals,  M.  Demeny  believed 
that  he  detected,  even  inordinary  walking,  a  short  period  during  which 
both  feet  were  simultaneously  on  the  ground,  and  that  this  period  was 
prolonged  as  the  pedestrian  became  more  tired.  These  results  would 
be  most  important  if,  so  to  speak,  they  provided  a  means  of  measuring 
fatigue. 


134  MOVEMENT 

place  in  three  directions  of  space,  and  thus  require 
simultaneous  registration  by  three  curves. 

Nevertheless,  our  late  pupil  and  friend,  Carle t,* 
obtained,  by  the  geometrical  combination  of  three 
curves  recorded  simultaneously,  the  actual  path 
described  by  a  selected  point  on  the  body  of  a  man 
walking.  A  movement  of  this  nature  can  only  be 
represented  by  a  solid  figure. 

Carlet  used  for  this  purpose  a  piece  of  wire  twisted 
in  different  directions.  A  flat  figure,  even  with  the 
help  of  light  and  shade  (Fig.  91),  can  only  give  a  very 
imperfect  representation  of  a  movement  of  this  kind. 


Fig.  91. — The  trajectory  of  the  pubis  of  a  man  at  a  walking  pace.  A  metal  wire 
twisted  in  various  ways  indicates  the  variations  of  this  curve  in  respect  to  the 
three  directions  of  space. 

►Stereoscopic  images  alone  are  capable  of  giving  a 
satisfactory  picture  of  it.  Now,  we  said  in  Chapter  II. 
how  easily  images  of  this  kind  might  be  obtained. 
Fig.  14  shows  a  trajectory  very  similar  to  that 
laboriously  obtained  by  Carlet. 

AVhen  it  is  a  matter  of  registering  all  the  details 
of  a  man's  movements,  both  as  regards  change  of 
position  and  attitude  of  the  body  and  limbs,  mechanical 
registration  is  out  of  the  question.  It  is  at  this  point 
that  chronophotography  comes  to  the  rescue. 

The  Study  of  Movements  in  Man  by  means  of  Chrono- 
photography on  Fixed  Plates.  —  In  Chapter  II.  we 
showed  how  to  obtain  on  -fixed  plates  a  series  of  images 
corresponding  to  the  successive  phases  of  a  movement, 

*  Carlet,  "  Essai  Experimental  sur  la  Locomotion  de  1' Homme," 
Annates  des  Science*  \aturelles,  1872. 


HUMAN   MOVEMENTS  135 

and  we  gave  as  examples  chronophotographic  repre- 
sentations of  walking  and  running.  Fig.  92  shows 
how  a  long-jump  is  executed.  The  figures  in  the 
photograph  reveal  attitudes  which  the  eyes  are  not 
accustomed  to  see ;  they  express  better  than  language 
the  way  in  which  the  movement  is  executed,  and  allow 
the  different  phases  to  be  followed  with  ease.  In 
certain  respects  they  correct  ideas  which  existed  on 
the  subject  of  the  mechanism  of  jumping.  Take,  for 
instance,  the  theory  which  led  teachers  of  gymnastics 
to  recommend  their  pupils  to  land  on  the  toes  in  order 
to  break  the  shock  on  coming  in  contact  with  the 
ground.  Our  figures  show,  on  the  contrary,  that  in 
long-jumping  it  is  the  heels  which  first  reach  the 
ground,  and  that  it  is  the  flexion  of  the  legs  and 
thighs  that  breaks  the  shock.  To  sum  up,  chrono- 
photography  affords  the  means  of  understanding  the 
real  characters  of  a  movement,  and  is  therefore  of 
value  in  teaching  athletic  exercises.  Guided  by  photo- 
graphs of  this  sort,  it  is  easy  to  imitate  the  style  of 
walking  or  running  set  by  the  person  who  serves  as 
a  model,  and  to  reproduce  his  method  of  extending 
or  flexing  the  limbs,  of  swinging  the  arms,  and  of 
bringing  the  feet  to  the  ground  or  removing  them 
from  it.  It  would  be  much  more  difficult  to  imitate 
these  movements  by  merely  watching  the  instructor, 
because,  especially  in  rapid  movements,  the  motions 
are  so  transitory  as  to  escape  observation. 

In  Fig.  92  the  number  of  images  is  only  five  to  the 
second ;  this,  however,  is  sufficient  to  show  the  series 
of  actions  which  must  be  accomplished  in  executing 
a  jump  of  this  kind.  By  looking  at  these  images  in 
the  order  of  execution,  it  is  seen  that  the  jumper 
acquires  by  a  preliminary  run  sufficient  impetus  to 
cover  a  considerable  distance  during  the  period  of 
suspension. 


136 


MOVEMENT 


HUMAN  MOVEMENTS  137 

At  the  moment  of  jumping,  the  leg  in  contact  with 
the  ground  is  violently  extended,  thereby  imparting 
a  vertical  impetus  to  the  body,  at  the  same  moment 
the  arms  are  thrown  up,  giving  additional  energy  to 
the  effort. 

The  successive  images  show  the  jumper  after  he 
has  left  the  ground,  with  the  arms  elevated  in  front 
and  the  legs  separated ;  later  on,  the  arms  drop,  and 
the  legs  are  brought  nearer  together  as  they  become 
more  advanced  in  front  of  the  body,  so  that  finally  the 
heels  of  both  feet  touch  the  ground  together,  and  in 
front  of  the  centre  of  gravity  of  the  body.  A  fall  on 
the  face  is  thus  obviated.  At  the  moment  of  descent 
the  legs  are  flexed,  so  as  to  counteract  the  impetus 
of  the  body. 

The  distance  cleared  is  more  or  less  extensive, 
according  as  this  series  of  actions  is  skilfully  or 
clumsily  executed,  and  according  as  the  jumper  lands 
advantageously  on  the  ground  or  the  reverse.  If  he 
has  miscalculated  his  speed,  and  his  feet  are  not 
sufficiently  far  advanced  in  front  of  him  at  the 
moment  of  landing,  he  cannot  retain  his  balance,  but 
has  to  run  forward  a  few  steps  until  the  impetus  is 
checked. 

In  the  case  of  pole-jumping  (Fig.  93),  it  is  equally 
easy  to  follow  the  various  stages.  The  jumper  fixes 
the  end  of  his  pole  in  the  ground,  and  at  the  same 
time  raises  himself  by  a  vigorous  extension  of  the 
legs.  The  combined  action  of  the  vertical  and  hori- 
zontal impulses  imparted  to  the  body  enables  it  to 
describe  an  arc  of  a  circle.  In  falling,  the  body  will 
continue  this  curve,  and  will  land  just  as  far  in  advance 
of  the  point  of  the  pole  as  it  was  behind  it  at  starting. 
But  a  skilful  jumper  can  avail  himself  of  an  artifice 
which  enables  him  to  augment  his  jump  considerably. 
It   consists    in    elongating    the    radius   of   the   circle 


138 


MOVEMENT 


HUMAN   MOVEMENTS  139 

described  by  climbing  up  the  pole  at  the  moment  it 
passes  the  vertical,  and  then  by  inclining  the  body 
until  it  becomes  almost  horizontal,  that  is  to  say,  at 
right  angles  to  the  radius  of  the  circle  described,  the 
jumper  falls  naturally  on  his  feet  at  a  much  greater 
distance  from  the  starting-point. 

In  pole-jumping,  the  initial  impetus  is  not,  as  in 
the  case  of  long-jumping,  the  only  force  upon  which 
the  extent  of  the  jump  depends ;  but  this  distance 
can  be  augmented  by  manoeuvres  of  the  jumper,  who 
can  make  use  of  his  arms  by  employing  the  pole  as 
a  fixed  point  of  support  while  he  is  still  in  the  air. 

For  a  more  detailed  study  of  movements  in  physical 
exercises,  recourse  must  be  had  to  those  outline  or 
geometrical  photographs  of  which  we  have  already 
given  an  example  in  the  case  of  a  man  walking.  A 
man  dressed  in  black  velvet  with  bright  lines  down 
his  arms  and  legs  produces  Fig.  94  as  the  result  of 
a  long-jump  preceded  by  a  preliminary  run. 

Here  all  the  phases  of  the  movement  are  arranged 
in  close  series  with  no  sudden  transitions,  because  of 
the  great  number  of  images  (twenty-rive  to  the  second) 
taken  during  the  jump. 

In  order  to  render  chronophotographs  of  movements 
more  instructive,  these  images  should  be  taken  from 
very  strong  and  competent  athletes ;  for  example, 
from  the  prize-winners  at  athletic  sports.  These 
champions  will  thus  betray  the  secret  of  their  success, 
perhaps  unconsciously  acquired,  and  which  they  would 
doubtless  be  incapable  of  defining  themselves. 

The  same  method  could  equally  well  be  applied  to 
the  teaching  of  movements  necessary  for  the  execu- 
tion of  various  skilled  industries.  It  would  show  how 
the  stroke  of  a  skilful  blacksmith  differed  from  that  of 
a  novice.  It  would  be  the  same  in  all  manual  per- 
formances, and  in  all  kinds  of  sport. 


140 


MOVEMENT 


HUMAN  MOVEMENTS 


141 


Fig.  95.— Fencing.     Kead  from  below  upwards. 


11 


142 


MOVEMENT 


From  a  series  of  diagrams  of  the  kind,  we  have 
easily  been  able  to  follow  the  successive  actions  of  a 
man  mounting  a  bicycle.  The  study  of  these  figures 
would  be  an  excellent  preparation  for  any  one  wishing 


-l--~?Wvi-£ '-it&'i'^S.  ?•"*  v-  -"•  •. '.  -~ ~T.-' - V  v*  "•"■' 


/.. 


/  Mann  wv 


Fig.  96.— Jump  from  a  height  wit'i  flexion  of  the  legs  to  break  the  fall 

to  learn  exercises  of  this  kind.  In  all  trials  of  strength, 
and  in  fencing,  certain  actions  occur  which  the  eye  is 
unable  to  follow  and  language  fails  to  express.  If  an 
attempt  is  made  to  teach  them  by  executing  them 
slowly,  their  whole  character  is  completely  changed. 


HUMAN   MOVEMENTS 


143 


Here,  again,  a  series  of  photographs,  taken  at  the  rate 
of  10  to  20  per  second,  helps  to  explain  all  the  details 
of  the  movement. 

Unfortunately,  we  could  not  represent  a  whole  series 


« --- — *     \ 

,\ >       \ 


liiiHi  \  [Hi 


5 


T*m 


*r.r. 


I 


Fig.  97. — Jump  from  a  height  with  stiffened  legs. 


of  this  kind  in  the  compass  of  this  book,  and  we  can 
only  give  a  few  fragmentary  examples.  We  have 
already  shown  in  Fig.  86  three  successive  phases  of 
broad-sword-exercise.     Fig.  95    similarly  shows   three 


144 


MOVEMENT 


instantaneous  views  of  two  men  fencing;  both  sets 
of  combatants  represented  belonged  to  the  Italian 
school. 

Geometrical  photographs  sometimes  elucidate  ex- 
tremely complicated  movements.  Thus,  in  jumping 
from  a  height  (Fig.  96),  the  position  of  each  point  of 
the  body,  in  its  various  phases  of  movement,  is 
expressed  by  an  almost  continuous  curve.  The  axes 
of  the  long  bones  make  the  figures  more  or  less  com 
plicated,  revealing  movements  the  existence  of  which 
would  never  have  been   suspected   from    mere   ocular 


Fig.  98.—  Oscillations  of  the  leg  in  running.     (Geometrical  chronophotograph.) 

observation.  In  jumping  from  a  height,  the  difference 
between  landing  gently  with  no  shock  and  landing 
with  rigid  legs  is  clearly  seen  by  comparing  Fig.  96 
with  Fig.  97.  The  latter  corresponds  to  the  drop  with 
stiffened  legs,  namely,  in  which  the  shock  is  not 
broken  by  flexion  of  the  legs. 

In  complicated  actions,  a  diagram  can  be  obtained 
of  only  one  part  of  a  movement ;  for  instance,  in 
running  it  may  only  be  necessary  to  observe  the  phases 
of  oscillation  of  the  legs — this  can  be  done  by  limiting 


HUMAN   MOVEMENTS  145 

the  diagram  to  the  movements  of  the  extremities  in 
question.  Fig.  98  shows  the  movements  of  a  leg  in 
running.  The  sets  of  dotted  lines  show  at  any  par- 
ticular moment  the  angle  formed  by  each  segment  with 
the  vertical,  as  well  as  the  path  followed  by  each  joint. 
In  geometrical  photographs,  thanks  to  the  great 
number  of  the  images,  the  discontinuity  of  the  phases 
almost  entirely  disappears,  and  the  actual  path  followed 
by  each  part  of  the  body  can  be  seen  represented 
almost  as  a  continuous  curve.  These  indications  are 
most  useful  in  studying  movement  from  the  point  of 
view  of  dynamics,  for  by  them  the  velocity  as  well  as 
the  acceleration  of  the  body  mass  can  be  measured. 


CHAPTER  IX 

CERTAIN   MOVEMENTS   IN    MAN 
From  the  Point  of  View  of  Dynamics 

Summary. — Object  of  dynamics — Measurement  of  the  forces  which 
play  a  part  in  human  locomotion— Traction  dynamograph — 
Dynamograph  for  expressing  the  amount  of  pressure  exercised 
by  the  feet  on  the  ground— Combination  of  the  dynamograph 
with  a  method  of  recording  movements — The  laws  of  ballistics  as 
applied  to  the  mechanism  of  jumping — Combined  employment  of 
dynamograpliy  and  chronophotography— Mechanical  work  done 
ill  human  locomotion;  work  in  the  vertical  direction;  work  in 
the  horizontal  direction;  work  done  in  maintaining  the  move- 
ment of  the  lower  limbs  during  their  period  of  suspension — 
Relative  amount  of  work  done  during  different  kinds  of  paces 
— Practical  applications. 

The  movement  of  a  solid  body,  and  the  force  which 
produces  it,  are  necessarily  closely  associated,  so  that 
knowledge  of  movement  implies  knowledge  of  force, 
and  vice  versa.  At  the  same  time,  in  practice  it  is 
easier  to  measure  force  directly  by  means  of  the 
dynamometer. 

Now,  in  human  locomotion,  the  forces  which  are 
concerned  are  ever  variable  quantities,  and  to  thoroughly 
understand  each  individual  phase,  a  registering  appa- 
ratus which  affords  a  continuous  record  must  be  em- 
ployed. Such  an  apparatus  is  called  a  "  dynamometer," 
and  indicates  by  the  variations  in  its  curve  the  amount 
of  force  which  acts  upon  it  at  any  particular  moment. 

Dynamometers  are  constructed  on  the  principle  that 


CERTAIN   MOVEMENTS   IN   MAN  147 

an  elastic  body  is  distorted  in  proportion  to  the  degree 
of  force  applied. 

We  have  endeavoured  to  use  dynamometers  of  uni- 
form pattern  throughout  our  researches  on  animal 
movements.  And  for  that  purpose  we  have  always 
employed  coils  of  indiarabber  tubing,  which  were 
more  or  less  compressed  according  to  the  external 
force  applied.  In  consequence  of  this  pressure,  the 
contained  air  was  more  or  less  squeezed  out  into  the 
chamber  of  a  recording  tambour. 

The  coils  of  tubing  of  which  the  dynamometer  is 
formed  are  wound  concentrically  like  the  spring 
of  a  watch.  The  central  end  is  closed,  and  the  peri- 
pheral or  free  end  communicates  with  the  chamber  of 
a  recording  tambour.  The  coil  itself  is  glued  on  to 
a  disc  of  cardboard. 

This  instrument  goes  by  the  name  of  "  The  spiral 
dynamometer."  The  tube  used  has  a  very  fine  bore 
with  very  thick  walls,  so  that  it  can  resist  strong 
pressure  without  bursting.  The  distortion  or  com- 
pression is  very  regular,  so  that  the  lever  of  the 
registering  tambour  is  practically  raised  to  a  height 
proportional  to  the  force  applied.* 

By  modifying  this  spiral  form,  we  were  able  to  con- 
struct a  traction  dynamograph  (Fig.  99).  The  latter 
apparatus  was  used  for  measuring  the  force  exercised  by 
horses  when  differently  harnessed.  One  of  the  ends  was 
securely  fastened  to  the  vehicle  and  the  other  to  the 
swing-bar.  Traction  on  the  part  of  the  horses  tended 
to  approximate  two  discs,  which  compressed  between 
them  the  turns  of  the  spiral  coil.f     The  air  expelled 

*  To  obtain  greater  accuracy  the  instrument  may  be  empirically 
graduated  by  applying  a  series  of  regularly  increasing  weights,  and 
marking  off  on  a  scale  the  corresponding  discursions  of  the  lever. 

t  We  proved  by  these  experiments  that,  if  the  traction  was  applied 
through  the  medium  of  elastic  tracts,  the  gradual  distribution  of 
the  shocks  thereby  occasioned  effected  a  great  economy  in  the  force 


148 


MOVEMENT 


from  the  spiral  reached  the  registering  tambour  by- 
means  of  a  tube. 

In  most  acts  of  human  locomotion  muscular  force 
manifests  itself  in  the  form  of  pressure ;  for  instance, 
this  is  the  case  when  a  man  extends  his  legs  from  a 
previous  position  of  flexion ;  as  the  legs  become  ex- 
tended, the  body  mass  is  repelled  in  an  opposite  direc- 
tion, because  the  feet,  resting  on  the  ground,  offer  a 
fixed  point  of  resistance. 

In  walking  or  running,  the  foot  presses  on  the  ground 


Fig.  99  —Traction  dynamograpb. 

with  a  force  equal  to  that  which  is  expended  in  moving 
the  body,  so  that  by  measuring  at  any  moment  the 
pressure  of  the  feet  on  the  ground,  we  also  measure 
the  force  expended  on  locomotion.  Our  spiral  dynamo- 
graph  is  a  useful  instrument  for  this  purpose. 

Dynamographic  Platform  for  Registering  the  Pressure 
of  the  Feet  on  the  Ground. — A  series  of  spirals,  similar 
to  those  previously  described,  are  arranged  on  an  oak 
platform    (Fig.    100).      One   of   these   spirals   is   left 


applied,  and  that  this  economy  might  even  amount  to  26  per  cent,  ot 
the  total  motive  force  (JMarey,  Trav.  du  Lalioratoire,  I87r>).  Wiist 
found  in  similar  experiments  a  saving  of  22  to  33  per  cent,  in  the 
work.  Kingelmann  has  noticed  an  economy  in  work  amounting  to 
something  like  50  per  cent. 


CEKTAIX    MOVEMENTS   IN   MAN 


149 


uncovered  so  that  the  tube  of  which  it  is  made  can  he 
seen,  the  others  are  placed  between  cardboard  discs. 
All  the  tubes  which  lead  from  these  spirals  unite  in 
a  common  collecting-tube  which  communicates  with 
the  chamber  of  the  recording  tambour.  A  plate  held 
in  position  by  metal  clips  accurately  covers  all  these 


Fi  -.  100.— Dynamographic  platform  for  giving  a  curve  of  foot-pressure  on  the  ground. 

spirals.     Such  is  the  general  structure  of  the  dynamo- 
graphic  platform.* 

When  a  man  mounts  this  platform  the  registering 
lever  is  raised  to  a  variable  height,  and  remains  in 
the  same  position  as  long  as  he  does  not  move. 
The  discursion  of  the  lever  expresses  the  weight  of 
the  body  ;  but  however  slightly  the  man  may  move,  the 

*  C.  B.  de  VAcadem.it  des  Sciences,  October  8,  1892. 


150  MOVEMENT 

amount  of  vertical  foot-pressure  on  the  platform  is 
altered  in  amount,  and  is  recorded  on  the  tracing  by 
the  lever.  The  following  is  the  law  which  governs 
the  variations  in  pressure  : — 

All  muscular  actions  ivhicli  alter  the  centre  of  gravity 
of  the  body  in  such  a  manner  as  to  raise  it  augment  the 
foot-pressure  on  the  ground. 

All  actions  tending  to  loiver  the  centre  of  gravity 
diminish  the  foot -pressure* 

The  dynamograph  which  measures  the  force  can  be 
employed  conjointly  with  an  apparatus  for  recording 
the  actual  movement.  It  can  be  seen,  then,  that 
mechanical  actions  accomplished  by  living  creatures 
obey  general  laws — amongst  others  those  of  ballistics. 

Now,  in  order  to  determine  the  phases  of  a  move- 
ment, two  methods  may  be  employed,  either  that  of 
mechanical  registration  or  that  of  geometrical  chrono- 
photography. 

Mechanical  Record  of  a  Movement. — Movements,  such 
as  we  shall  have  to  deal  with,  are  generally  too 
extensive  to  be  directly  recorded  by  means  of  a 
tracing  needle.  In  jumping,  for  instance,  the  head 
may  be  elevated  any  distance  between  30  and  50 
centimetres  in  a  vertical  direction.  This  movement 
must  be  reduced  to  such  proportions  as  can  be  regis- 
tered on  the  surface  of  a  revolving  cylinder.  This 
reduction  can  be  effected  by  means  of  the  elastic- 
thread  method  previously  described  (Fig.  29). 

If  a  man  stands  on  the  platform  of  a  dynamograph, 
and  wears  a  very  tight-fitting  cap,  the  elastic  thread 
may  be  fastened  at  one  end  to  the  cap,  and  at  the 
other  to  a  solid  support  by  means  of  a  clip  (Fig.  101). 
This  thread  may  be  fixed  near  its  upper  end  to  the  lever 

*  All  effects  which  are  produced  during  the  performance  of  a 
movement  are  followed,  when  the  movement  is  concluded,  by  counter 
effects  in  the  opposite  direction. 


Fig.  101.— Method  of  simultaneously  recording  the  foot  pressure  on  the  ground  and 
the  changes  in  elevation  of  the  body  during  a  jump. 


152 


MOVEMENT 


of  a  tambour.  Two  recording  tambours  register  two 
curves  on  a  revolving  cylinder,  one  the  curve  of  foot- 
pressure,  and  the  other  that  of  the  vertical  discursions 
of  the  head. 

Examination  of  these  curves,  enlarged,  if  necessary, 
si  lows  that  in  all  respects  the  laws  of  animal  move- 
ments conform  to  general  laws— in  this  case  to  the  laws 
of  ballistics. 

The  areas  of  the  curves  which  are  described  by  the 


Fig.  102.— Superior  curves;  changes  of  height  in  the  head  during  the  jump.  The 
ordinate*  DC  and  l)U'  are  proportional  lo  the  height  of  the  j  imp. 

Inferior  curves;  pressure  exercised  by  the  feet  on  the  ground.  The  shaded  areas 
show  the  quantity  of  mow.  mad  communicated  to  the  body  in  the  two  jumps. 


dynanx (graphic  needle  express  the  exact  equivalent  of 
the  force  employed  in  the  effort  of  jumping.  And  it 
is  found  that  when  two  such  areas  differ,  their  ratio 
to  one  another  is  as  the  square  root  of  the  height 
jumped.  If  the  area  of  the  curves  be  the  same,  no 
matter  what  be  the  shape,  the  heights  of  the  jumps 
must  be  the  same.  If  two  men  of  different  weights 
jump  the  same  height,  the  areas  of  the  dynamographic 


CERTAIN  MOVEMENTS   IN   MAN  153 

curves  are  in  proportion  to  the  weight  raised.  On 
comparing  the  curve  of  the  height  jumped  with  that 
of  the  dynamograph,  it  is  found  that  it  is  not  the 
absolute  initial  energy  of  the  effort  which  conditions 
the  height  of  the  jump,  but  the  amount  or  quantity 
of  force  expended,  namely,  the  product  of  the  force 
and  the  duration  of  the  effort ;  in  other  words,  the  area 
of  the  curve. 

Sometimes  the  lowest  jumps  correspond  to  curves 
which  show  great  initial  effort,  but  sustained  only  for 
a  brief  moment.  In  fact,  areas  of  different  curves, 
which  represent  jumps  of  equal  height,  may  be  infinitely 
varied ;  a  violent  and  brief  effort  producing  the  same 
effect  as  one  initially  feeble  but  longer  sustained. 

Combined  Employment  of  Dynamography  and  Chrono- 
photograpby. — Mechanical  registration  of  movement  is 
not  always  feasible;  for  instance,  in  the  case  of  a  man 
walking,  it  is  difficult  to  register  all  the  movements  of 
the  different  parts  of  the  limb.  Chronophotography 
comes  to  the  rescue,  and  this  method  can  be  combined 
with  the  employment  of  the  dynamograph.  Let  us 
suppose  that  we  want  to  discover  with  what  force  the 
foot  presses  on  the  ground  during  the  different  phases 
of  flexion  and  extension  of  the  leg,  provided,  of  course, 
that  the  foot  never  leaves  the  ground  during  the  period 
under  observation.  The  application  of  the  chrono- 
photograph  combined  with  the  dynamograph,  at  once 
suggests  itself,  the  former  recording  the  movements 
executed  by  the  leg  during  half  a  step  (Fig.  103),  and 
the  latter  the  degree  of  pressure  exercised  during  the 
same  period  (Fig.  104). 

It  is  now  necessary  to  establish  the  connection 
between  the  various  chronophotographic  images  and 
the  corresponding  elements  of  the  dynamographic 
curve.  For  this  purpose  we  must  count  in  Fig.  103 
the  number  of  images  which  correspond  to  the  phase 


151 


MOVEMENT 


of  downward  pressure  of  the  foot.  It  is  found  to  be 
twelve.  It  is  clear,  then,  that  the  dynamographic 
tracing,  taken  as  a  whole,  corresponds  to  this  total 
period  occupied  by  the  leg  in  its  phase  of  downward 


Fig.  I03.-Geometrical  chronophotocraph  of  the  movements  of  the  leg  in  walking, 
during  the  period  that  the  foot  is  in  contact  with  the  ground. 

pressure,  so  we  must  divide  the  abscissa  of  this  curve 
into  twelve  equal  parts.  If  we  draw  the  twelve  cor- 
responding ordinates,  each  of  them  will  express  the 
vertical  force  exercised  by  the  foot  on  the  ground  for 


^ 


Fig.  104.— Dynamographic  tracing  to  express  the  phases  of  pressure  hy  the 
foot  on  the  ground  in  walking. 

the  corresponding  position  of  the  leg.  If  these  two 
sets  of  figures  are  correspondingly  numbered  in  the 
tracings,  comparison  is  greatly  facilitated. 

One  can,  if  so  desired,  dispense  with  the  dynamo- 


CERTAIN"   MOVEMENTS  IN  MAN 


155 


graph,  and  measure  the  force  expended  from  the  data 
afforded  by  the  geometrical  chronophotographs ;  in 
short,  when  the  body  mass  is  known,  as  well  as  the 
position   and   movements   of  the    centre    of   gravity, 


i 


/  i  \ 
'    :    S 

/     i     \ 


Shovtdei 

i 

i 


,    mp 


Fig.  105.— Geometrical  chronophotograph  of  the  movements  executed  in  taking  a  high-jump. 

the   force   expended    on   the  movement   can   also   be 
calculated. 

Mechanical  Work  done  by  Man  in  Walking. — In  view 
of  the  fact  that  it  is  possible  to  estimate  the  work 
done   in  jumping  by  means   of  geometrical   chrono- 


156  MOVEMENT 

photographs  (Fig.  105),  it  is  easy  to  predict  that  the 
same  method  might  be  applicable  in  the  case  of  various 
kinds  of  paces. 

So  far  physicists  have  only  calculated  the  amount 
of  energy  expended  or  gained  by  a  man  in  walking 
along  an  inclined  plane,  in  terms  of  the  body  weight 
lifted  or  lowered  such  and  such  a  height.  The  first  is  a 
case  of  positive  energy,  and  the  second  one  of  negative 
energy.  The  amount  of  energy  expended  in  different 
directions  is  the  product  of  the  body  weight  and  the 
height  of  lift,  an  amount  which  is  expressed  in  kilo- 
grammetres.  Looking  at  the  matter  in  this  light, 
progress  along  level  ground  would  require  no  apparent 
expenditure  of  energy,  and  yet  it  is  accompanied  with 
muscular  exertion  and  consequent  fatigue. 

We  thought  it  was  possible  to  estimate  approxi- 
mately the  mechanical  energy  expended  in  walking 
or  running  along  horizontal  ground  by  observing  the 
movements  transmitted  in  various  directions  to  the 
body  by  the  muscular  actions  involved.  If  the  move- 
ments of  the  centre  of  gravity  of  the  body  could  be 
followed  in  space,  they  would  be  seen  to  constitute  a 
series  of  vertical  oscillations  in  accordance  with  the 
movements  of  the  feet.  At  the  same  time  during  each 
oscillation  there  is  a  certain  movement  of  translation, 
sometimes  at  an  increased  and  sometimes  at  a  decreased 
velocity.* 

Another  way  in  which  energy  is  expended  is  when 
movements  are  alternately  communicated  to  the  legs, 
movements  which  gravity  might  account  for  if  they 
were,  as  the  brothers  Weber  believed,  comparable  to 
oscillations  of  a  pendulum.  In  practice,  however,  these 
movements  usually  require  the  help  of  the  muscles. 

The  measurements  (Fig.  106)  of  different  movements 

*  We  ignore  as  unimportant  the  movements  of  the  centre  of  gravity 
which  occur  outside  the  vertical  piano  of  progression. 


CERTAIN   MOVEMENTS   IN    MAN 


157 


of  the  human  body  and  limbs  in  the  act  of  walking 
have  been  obtained  by  means  of  chronophotography. 


Three  principal  elements   are   involved  in  the  work 
which  is  done  during  the  act  of  walking  on  the  level. 
A.  Vertical  work. 
12 


158 


MOVEMENT 


B.  Horizontal  work. 

C.  Work  expended  on  keeping  up  the  oscillations 
of  the  legs^Luring  their  period  of  suspension. 

A.  Muscular  Work  done  in  a  Vertical  Direction. — 
The  movements  of  the  head  are  practically  the  same 
as  those  of  the  centre  of  gravity.  Now,  the  trajectory 
of  the  head-movements  is  an  undulating  curve  (Fig. 
107),  which  periodically  reaches  its  maximum  as  the 
foot  arrives  at  the  mid  phase  of  contact,  and  similarly 
reaches  its  minimum  at  the  mid  phase  of  suspension.* 

The  parallel  and  dotted  lines  (Fig.  107),  which  are 
tangents  to  the  upper  and  lower  limbs  of  this  curve, 
afford   a   measure,   by   the   distance   which   separates 


rrr 


:t- 


Fig.  107.— Vertical  oscillations  of  tlie  head  when  walking. 

them,  of  the   extent   of  the   vertical   oscillations   of 
the  body. 

To  measure  the  absolute  extent  of  these  discursions, 
a  transparency  of  Fig.  107  is  thrown  on  the  screen, 
and  enlarged  by  means  of  an  optical  arrangement  to 
its  actual  dimensions,  so  that  the  extent  of  a  vertical 
oscillation  corresponds  to  the  length  of  half  a  step 
measured  on  the  ground.  The  work  done  each  time 
the  body  is  elevated  or  depressed  can  be  estimated 
by  multiplying  the  weight  of  the  pedestrian  by  the 
vertical  height  which  separates  the  dotted  lines  in  the 


*  On  the   other  hand,  in  running,  the  maximum  corresponds  to 
the  period  of  suspension,  and  the  minimum  to  the  period  ol  contact. 


CERTAIN  MOVEMENTS  IN   MAN  159 


enlarged  figure.  So  that,  if  the  weight  is  75  kilo- 
grams,  and  the  amplitude  of  the  oscillations  0*04 
of  a  metre,  each  elevation  of  the  body  wi^l  represent 
3  kilogrammetres  of  positive  work,  and  each  depres- 
sion the  same  amount  of  negative  work.  As  there  are 
two  double  oscillations  of  this  kind  in  a  completed 
step,  the  muscular  work  corresponding  to  the  verti- 
cal oscillation  will  be  12  kilogrammetres  for  each 
step.* 

B.  Muscular  Wtrk  expended  on  Movement  in  a 
Horizontal  Direction  in  Walking. — The  velocity  of  the 
horizontal  movement  of  the  body  is  subject  to  periodic 
variations,  and  hence  there  must  be  periodic  variations 
in  the  energy  required,  in  proportion  to  the  work 
executed  in  the  different  phases  of  foot-contact,  whether 
this  work  be  represented  by  movement  or  by  resistance. 
These  variations  in  speed  are  deduced  from  the  degree 
of  separation  of  the  points  on  the  trajectory,  because 
these  points  are  photographed  at  equal  intervals  of 
time,  lor  instance,  at  intervals  of  -^  of  a  second.  The 
horizontal  projection  of  these  intervals  allows  one  to 
construct  the  velocity  curve  of  the  horizontal  move- 
ment by  taking  as  ordinates  lengths  which  correspond 
to  the  distances  which  separate  the  points,  that  is  to 
say,  which  correspond  to  the  velocity. 

From  the  maximum  and  minimum  velocities  of  the 
body  mass,  the  corresponding  measure  of  the  energy 
expended  can  be  deduced.  The  energy  developed 
by  muscles  both  in  producing  movement  and  in 
offering  resistance  is  equal  in  each  case  to  half  the 
variation  of  the  vital  force.  So  that  the  total  sum 
of  these  two  forms  of  energy  can  never  exceed  the 

*  This  estimate,  namely,  the  body  weight  multiplied  by  twice  the 
height  of  the  vertical  oscillation,  is  an  inexact  valuation,  which  does 
not  really  give  the  expenditure  of  muscular  force  :  a  certain  portion  of 
the  energy  seems  to  store  itself  up  in  the  muscles  during  each  period 
of  descent,  and  to  be  liberated  in  the  next  phase  of  ascent. 


160  MOVEMENT 

amount  of  the  whole  force  expended,  that  is  to  say, 
for  the  case  in  point,  2*5  kilogrammetres. 

C.  Muscular  Work  done  in  moving  each  of  the  Lower 
Limbs  during  the  Period  of  Suspension. — The  compli- 
cated movements  of  the  lower  extremities  correspond 
to  those  of  a  pair  of  double-jointed  pendulums  in 
unstable  equilibrium  :  they  are,  however,  not  only  acted 
upon  by  gravity,  but  also  by  muscular  contractions, 
while  the  point  of  suspension  itself  moves  with  a 
variable  motion  along  a  curvilinear  trajectory. 

The  method  employed  for  measuring  the  energy 
expended  on  these  oscillations  consists  in  measuring 
the  moment  of  inertia  of  the  lower  limbs  in  reference 
to  the  axes  of  rotation,  and  by  measuring  on  geo- 
metrical diagrams  the  angular  velocity  which  they 
acquire.  The  result  thus  obtained  is  very  small,  0*3 
of  a  kilogrammetre  for  each  step.  Thus  the  most  un- 
certain determination  in  these  measurements  is  prac- 
tically a  negligible  quantity,  and  only  very  slightly 
influences  the  total  amount  of  energy  expended  on 
each  step.* 

According  to  the  estimates  indicated  above,  the  total 
amount  of  energy  expended  on  a  step  is  9  kilogram- 
metres.  But  even  the  most  exact  measurement  of  the 
energy  expended  in  any  particular  kind  of  pace  is 
much  less  interesting  than  the  study  of  the  actual 
variations  in  the  amount  of  work  done  as  the  pace 
is  accelerated.  If  we  calculate  the  total  energy 
expended  in  fast  running,  the  amount  will  be  found 
to  be  very  different  from  that  expended  on  slow 
progression.      The    following    are    the    estimates    for 


*  The  practical  importance  of  an  exact  determination  of  the  energy 
is  very  great;  it  is  also  most  desirable  that  all  the  papers  we  possess 
on  this  subject  at  the  Physiological  Station  should  be  agnin  studied 
by  the  most  approved  methods.  This  subject  is  worthy  of  the  con- 
sideration of  the  greatesl  mathematicians 


CERTAIN  MOVEMENTS   IS  MAX  161 

kilogrammetrcs. 

Translation  of  the  lower  limb  Hi 

Vertical  oscillations  of  the  body      2  3 

Acceleration    nn<l    remissions   in    velocily   in   the 

horizontal  direction        IS  4 

Total         ...     241 

Thus  the  expenditure  of  energy  in  taking  half  a 
step  on  level  ground  varies  according  to  the  gait  from 
9  to  24  kilogrammetres.  If  account  is  kept  of  the 
number  of  steps  taken  in  a  minute  in  these  two 
extreme  cases,  the  expenditure  of  energy  will  be  found 
to  be,  in  slow  walking  720  kilogrammetres,  and  in 
rapid  running  6748  kilogrammetres,  which  represents 
about  12  kil  >grammetres  per  second  in  the  first  case, 
and  112  kilogrammetres  in  the  second.* 

*  We  knew  perfectly  well  that  walking  on  level  ground  represented 
the  expenditure  of  a  certain  amount  of  energy,  and  tried  to  estimate 
the  exact  amount,  but  that  did  nut  necessarily  imply  any  difference 
of  opinion  between  physicists  and  physiologists.  If  physicists  only 
took  account  of  the  energy  expended  in  walking  when  the  road  was 
inclined,  it  was  because  only  in  this  case  could  tiny  ascertain  the 
exact  amount  of  work  done,  namely,  that  required  for  lifting  the 
body  weight  through  a  certain  number  of  metres,  or  lowering  it  as 
the  case  might  be. 

But  Coulomb  knew  full  well  that  both  in  walking  and  in  carrying 
burdens  the  muscles  developed  energy  and  did  work,  but  not  being 
able  to  reduce  this  expenditure  of  energy  to  the  usual  formula  PH, 
he  gave  it  the  name  of  '*  Useful  effect,"  (PE),  that  is  to  say,  the  wt  ight 
multiplied  by  the  distance  traversed.  In  short,  the  measurement  of 
energy  in  walking  and  running  on  level  ground  demands  a  complete 
knowledge  of  the  movements  transmitted  to  the  body  and  limbs  as 
the  foot  is  lifted  from  the  ground. 

It  was  for  physiologists  to  determine  these  movements,  ami  as 
we  have  seen,  chronophotography  afforded  them  an  excellent  means 
of  so  doing. 

In  giving  the  above  measurements  of  the  work  performed  in  walking, 
we  said  that  they  probably  represented  the  maximum,  and  that  their 
real  value  was  perhaps  something  less.  This  is  because  in  alternate 
movements  in  contrary  directions  there  may  be  a  certain  storage  of 
energy  in  the  organs  which  execute  the  movements,  and  consequently 
there  may  be  a  certain  suppression  of  energy  which  would  other- 
wise be  expended,  and  consequently  in  the  succeeding  action  there 
may  be  a  certain  amount  of  restitution.  To  make  our  point  clear, 
let  us  take  the  case  of  an  elastic  ball  falling  on  a  hard  surface 
from  a  certain  height.  Let  us  suppose  the  ball  weighs  100  grams, 
and  that  it  falls  through  a  distance  of  one  metre.  As  the  ball  readies 
the  ground,  the  action  of  gravity  will  have  produced  work  to  the 


162  MOVEMENT 

Relative  Amount  of  Work  done  in  executing  Various 
Paces. — If  the  values  of  the  different  factors  constituting 

extent  of  100  grammetres.  But  let  us  go  a  little  further.  The  ball 
in  consequence  will  be  flattened  against  the  ground,  and  rebouud  to 
a  certain  height,  0*00  metre  for  instance.  When  the  ball  has  reached 
this  height,  of  the  energy  which  1ms  accrued  from  the  effects  of 
gravity,  only  40  grammetres  have  been  expended,  beeause  on  letting 
it  fall  down  again  we  shall  find  that  there  are  GO  grammetres  of 
energy  left.  These  60  grammetres,  then,  were  recovered  by  the  elastic 
force  of  the  ball,  which  had  stored  them  up. 

Is  there  anything  analogous,  when  at  the  end  of  a  movement  the 
antagonistic  muscles  tend  to  slop  it ;  and  will  these  muscles  contribute 
anything  towards  the  succeeding  movement  in  the  opposite  direction  ? 
The  following  facts  lead  us  to  be  ieve  that  there  is  such  a  restitution. 

When  one  exerts  one's  self  to  jump  and  reach  an  object  above 
one's  head,  if  the  first  attempt  is  unsuccessful,  fcometimes  the  second 
succeeds. 

Chronophotography  shows  that  the  second  jump  is  always  higher 
than  the  first.  What  is  it  that  occurs  in  such  successive  acts?  In 
the  first  jump,  the  total  effort  of  the  extensor  muscles  of  the  thighs 
and  legs  projects  the  body  a  certain  height.  In  descending,  these 
same  muscles  are  contracted  in  order  to  break  the  fall,  i.e.  in  order 
to  counteract  the  energy  generated  by  the  body.  Then  these  muscles 
are  again  contracted  to  project  the  body  into  the  air  a  second  time. 

Now,  since  the  height  of  the  second  jump  is  greater  than  the  first, 
it  must  be  admitted  that  the  elastic  force  of  the  muscles  which  are 
contracted  to  break  the  fall,  is  added  to  the  muscular  action  consciously 
brought  into  play  for  the  second  jump. 

Now,  is  this  elastic  force  of  rebound  due  to  a  physical  property  of 
the  muscles,  or  is  it  due  to  an  additional  expenditure  of  energy? 
Weber  demonstrated  that  a  muscle  when  in  action  acquired,  by  some 
intimate  change  within  its  fibres,  a  greater  elastic  force,  and  that  it 
was  this  force  which  produced  movement.  The  same  thing  happens, 
then,  in  a  living  tissue  as  in  a  steam-engine,  in  which  the  elastic  force 
of  a  gas  is  converted  into  work. 

Now,  from  the  physiological  point  of  view,  in  the  second  jump  theie 
was  no  obvious  liberation  of  stored-up  energy,  but  such  liberation  as 
there  was  must  have  been  the  result  of  intrinsic  action  accompanying 
all  muscular  contractions.  If  the  body  attained  to  a  greater  height  in 
the  second  jump  it  was  because  the  muscular  energy  was  greater.  We 
said,  however,  that  in  the  first  jump  we  exercised  our  muscles  to  the 
utmost  extent.  That  is  true,  but  it  u:ay  not  be  by  the  most  energetic, 
but  by  the  most  prolonged  effort  that  we  attained  to  so  great  a  height 
in  the  second  jump.  It  will  be  remembered  that,  in  the  experiments 
with  the  dynaniograph,  the  "area  of  impetus,"  or  the  amount  of 
movement  communicated  to  the  body,  was  proportional  to  the  square 
root  of  the  height  jumped;  and  that  the  height  of  the  jump  did  not 
depend  on  the  mere  height  of  the  dynamographic  curve,  because  the 
latter  only  expressed  the  degree  of  effort  at  one  particular  moment; 
the  duration  of  the  effort  had  also  to  be  taken  into  consideration.  For, 
as  we  mentioned,  often  the  highest  jumps  corresponded  to  curves  of 
the  lowest  amplitude. 


CERTAIN   MOVEMENTS   IN   MAN  163 

the  total  energy  expended  on  taking  a  step  are  com- 
pared, it  is  found  that  they  are  not  equally  (Fig.  108) 

It  is  necessary,  then,  to  know  whether  the  impetus  occasioned  by 
the  mubdes  has  not  lasted  longer  in  the  second  than  in  the  first 
jump. 

In  all  contracting  muscles,  the  elastic  force  starts  at  zero,  and 
attains  its  maximum  in  a  certain  time.  This  results  from  the  way  in 
which  the  contraction  is  produced,  namely,  by  a  gradual  summation 
of  a  series  of  contractions.  Nww,  if  we  leave  a  crouching  position  to 
jump  for  the  first  time,  our  extensor  muscles  gradually  contract,  and 
the-e  muscles  will  only  produce  their  maximum  effect  at  a  more  or 
less  advauced  phase  of  extension  of  ti.e  limbs. 

In  the  second  jump,  on  the  contrary,  when  in  breaking  the  fall  we 
again  assume  a  crouching  position,  our  extensor  muscles  i.ave  already 
reached  their  maximum  contracting  force;  and  it  is  this  maximum 
force  which  will  continue  to  operate  in  raising  us  up  again  until  we 
have  left  the  ground.  The  body  mass  will  have  received  the  full  effect 
of  the  muscular  contraction  during  a  longer  period,  and  consequently 
will  have  received  a  greater  "quantity"  of  movement. 

A  familiar  example  will  help  to  explain  the  difference  which  exists, 
as  far  as  intensity  of  result  is  concerned,  between  a  force  gradually 
developed  throughout  the  duration  "f  a  movement,  and  another  which, 
acts  with  all  its  intensity  during  the  whole  period  of  a  movement. 
When  we  wish  to  transmit  an  impetus  to  an  object  by  extending  a 
finger  we  y:ive  it  a  fillip.  That  is  to  say,  by  holding  the  last  phalanx 
of  tie  middle  finger  with  the  thumb,  and  strongly  contracting  the 
extensors  of  the  linger,  we  let  it  go  like  a  spring  at  the  moment  the 
maximum  degree  of  extension  is  reached.  The  obj'eet  is  thus  shot 
away  with  great  force.  The  impetus  would  have  been  very  muck 
weaker  if  the  middle  finger  had  previously  only  been  bent,  and  we 
had  then  suddenly  extended  it.  In  all  alternating  movements,  the 
muscles  work  to  better  advantage  than  in  simple  movements.  The 
brand^hing  of  a  weapon  before  striking  has  no  other  significance. 

Now,  since  the  work  done  by  a  muscle  is  the  same,  whether  it  is 
merely  work  of  resistance  or  work  represented  as  motion,  we  believe 
that,  if  we  want  to  estimate  the  work  done  in  walking,  we  are  justified 
in  doubling  the  v.due  of  e'jch  of  the  component  factors  of  the  wrork 
expended  in  maintaining  the  oscillations  of  the  body  and  limbs.  If 
we  said  that  the  estimate  thus  obtained  probably  represented  the 
maximum,  it  would  be  because  the  vital  energy  transmitted  to  the 
body  in  the  horizontal  d.rection,  and  that  transmitted  to  the  legs  at 
each  oscillation,  are  not  totally  expended  on  the  movements,  part 
being  lost  in  the  form  of  shocks  imparted  to  the  ground.  Yital 
energy  is  perhaps  stored  up  in  real  elastic  structures  of  the  body,  such 
as  tendons. 

Veterinary  experts  have  made  a  special  study  of  the  energy  lost  by 
the  hoofs  striking  the  ground  when  a  horse  is  travelling  at  a  rapid 
pace.  They  maintain  that  the  flexor  of  the  solitary  toe  which  consti- 
tutes the  foot  of  a  horse,  is  made  to  a  great  extent  of  elastic  tissue. 
It  possesses  in  consequence  a  physical  property  by  means  of  which  a 
more  or  less  important  part  of  the  vital  energy  lost  in  falling  ou  the 
feet  is  to  some  extent  returned  in  the  form  of  euergy. 


1G4 


MOVEMENT 


influenced  by  the  rate  of  progression.  Thus,  during 
slow  walking,  the  energy  expended  in  vertical  oscilla- 
tions is  relatively  greater  than  when  the  velocity  of 
horizontal  translation  is  increased ;  in  rapid  running, 
the  reverse    is   the   case.      It   is   necessary,  then,   to 


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length  of  step  (scale  iV>  n„__ 

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4b      4f     50      55       60      65      JO      ]5       60      b5      HO      95     -100    -105    -no 

Fro.  108.— Variations  in  the  vertical  oscillations  of  the  body  in  walking  and  in  running. 
The  rate  of  step  varies  bptween  40  and  130  per  minute.  Comparison  between  the 
curve  of  oscillation  and  that  of  the  length  of  stride. 


component  factors  of  the  work  undergo  when  under 
the  influence  of  a  gradual  acceleration. 

In  order  that  these  variations  might  be  clearly  un- 
derstood, they  have  been  represented  (Fig.  109)  in  a 
graphic  form.  In  constructing  these  curves,  the  num- 
ber of  steps  executed  in  a  minute  has  been  numbered 
off  on  the  abscissa.  The  corresponding  ordinates  were 
made  proportional  in  length  to  the  sum  of  all  the  factors 

This  subject  deserves  re-investigation.  It  would  be  interesting  to 
discover  whether  tendons  in  man  possess  this  valuable  property  to  any 
noticeable  degree,  and,  if  so,  whether  it  id  retained  throughout  life. 


CERTAIN   MOVEMENTS   IN   MAX 


1(35 


of  the  work.  Whatever  was  the  number  of  steps  per 
minute,  the  value  was  marked  off  on  the  ordinates 
from  below  upwards  always  in  the  same  order. 

1.  The  value  of  the  work  done  in  moving  the  lower 
extremity. 

2.  The  value  of  the  work  done  in  the  vertical  oscil- 
lation of  the  body. 

3.  The  work  done  in  accelerating  and  slowing  the 
horizontal  movement  of  translation. 


45    JO 


JO   JS    So    65  yo  g*  700  JOS'  110  US  tiO  12S  150  135  Mo  74S 


Ffg.  109. — Curves  of  the  different  elements  of  the  work  perf  rmed  in  walking  and 
running,  the  rate  of  prep  varying  from  40  to  145  per  minute  The  scale  to  the  left 
of  the  figure  indicates  the  number  of  kilogrammetres  expanded  on  each  step.  Eich 
of  the  ordinates  is  composed  of  three  separate  elements,  representing  the  value  of 
each  of  the  c  .mpo'ent  portions  of  the  total  work.  The  lowest  element  corresponds 
to  the  work  performed  by  the  oscillations  of  the  leg.  The  middle  (the  thick  line) 
represents  the  venical  oscillations  of  the  body.  The  superior  one  corresponds  to 
the  degree  of  acceleration  and  slowing  down  of  the  body  mass. 

On  the  curves  represented  in  Fig.  109,  the  different 
factors  in  the  work  apparently  vary  in  an  extraordinary 
fashion ;  but  these  variations  can  easily  be  accounted 
for  by  certain  considerations  from  the  point  of  view  of 
kinetics  or  dynamics.* 

*  To  quote  from  a  communication  made  to  the  Academie  des 
Sciences,  by  M.  Demeny  and  ourselves,  November  9,  18S5  : — 

A.    Variations  in  Work  (b-ne  in  moving  the  Lower  Limbs. — The  work 


166  MOVEMENT 

Practical  Applications. — The  data  afforded  by  these 
measurements  may  be  put  to  practical  use,  for  they 

performed  in  executing  these  movements  obviously  increases  in  pro- 
portion to  the  degree  of  acceleration  of  the  rate  of  step ;  but  a  fact 
which  is  at  first  surprising  is  that  for  the  same  number  of  steps  per 
minute  a  runner  expends  less  energy  than  a  pedestrian.  Thus,  at 
ninety  steps  a  minute,  a  man  would  expend  in  walking  1*4  kilogrmtrs 
in  the  movement  of  the  lower  extremity,  while  a  man  in  running 
would  only  expend  0\5  kilogrmtrs.  And  yet  the  actual  speed  at  which 
the  legs  move  in  running  is  greater  than  in  the  former  case. 

This  difference  is  because  the  speed  at  which  the  limbs  move  in 
reference  to  the  body  should  be  considered  by  itself  in  these  esti- 
mates.    Now,  the  speed  is  greater  in  walking  than  in  running. 

Indeed,  for  an  equal  number  of  steps  per  minute,  the  duration  of 
oscillation  of  the  lower  extremity  is  greater  in  proportion  as  the  period 
of  contact  of  the  foot  is  less.  The  period  of  contact  in  walking 
occupies  more  than  half  the  total  time  occupied  in  taking  one  step. 
In  running,  on  the  contrary,  the  duration  of  contact  is  always  less 
than  half,  and  as  the  angular  displacement  of  the  lower  extremity  is 
practically  equal  in  the  two  cases,  it  follows  that  the  velocity  of  move- 
ment of  the  legs  will  be  less  in  running,  because  the  period  of  oscilla- 
tion will  be  of  greater  duration.  A  physiological  result  of  this  in- 
equality in  the  duration  of  oscillation  of  the  limb  in  different  paces 
is  the  intuitive  tendency  to  begin  running  as  soon  as  the  rate  of 
walking  becomes  too  fast.  This  is  one  of  the  numberless  examples  of 
our  natural  instinct  to  expend  the  least  possible  effort  in  muscular 
actions. 

B.  Variation*  in  the  Work  don?  hy  the  Vertical  Oscillations  of  the 
Body. — This  factor  in  the  work  does  not  increase  regularly  with  the 
rapidity  of  footsteps.  In  walking,  the  work  rapidly  increases  between 
5.)  and  70  steps  per  minute  and  then  decreases.  In  running,  it  is  very 
geat  when  the  number  of  steps  per  minute  is  small,  and  diminishes  as 
the  rate  becomes  greater.  This  factor  in  the  total  work  done  depends 
on  the  weight  of  the  body  and  the  amplitude  of  tie  vertical  oscillations. 
The  difference  in  the  amount  of  work  performed  in  various  paces 
bears  a  direct  relationship  to  the  amplitude  of  the  above  oscillations. 

Photographic  and  mechanical  records  of  the  vertical  oscillations 
show  that  in  walking  there  is  a  relationship  between  the  length  of 
stride  and  the  amplitude  of  the  vertical  oscillations  of  the  body,  and 
since  we  have  proved  that  the  length  of  stride  increases  with  the 
rapidity  of  the  step  up  to  70  steps  per  minute,  and  then  diminishes 
rapidly  as  the  step  is  further  quickened,  it  naturally  follows  that  the 
work  corresponding  to  these  different  steps  varies  in  the  same  manner. 

In  running,  tne  work  done  is  greater  when  the  rate  of  step  is  slow, 
and  then  decreases  indefinitely.  The  corresponding  vertical  oscilla- 
tions vary  in  the  same  way.  The  body  being  suspended  in  the  air 
during  part  of  the  step  in  running  is  no  longer  constantly  influenced 
by  the  el  anges  in  the  directions  taken  by  the  limbs.  Consequently,  it 
is  the  duration  of  the  vertical  oscillation  which  regulates  the  amplitude. 
If  the  rate  of  step  is  slow,  the  body  must  be  elevated  very  high  so  that 
it  may  fall  slowly  on  to  the  limb  which  comes  in  contact  with  the  ground. 


CERTAIN    MOVEMENTS   IN   MAN  167 

indicate,  according  to  the  object  in  view,  the  best 
way  of  utilizing  muscular  force  in  walking  or  running  : 
whether  it  be  to  traverse  the  greatest  distance  with 
the  least  expenditure  of  energy,  or  whether  it  be  to 
cover  a  certain  distance  in  the  least  possible  time. 
Attention  should  not  only  be  directed  to  the  kind  of 
pace,  running  or  walking,  for  instance,  but  also  to  the 
number  of  steps  to  be  taken  in  the  minute. 

It  has  already  been  pointed  out  (Fig.  109)  that,  in 
walking  rapidly,  from  70  steps  per  minute  onwards,  the 
expenditure  of  energy  rapidly  increases,  and  that  in 
running  the  total  energy  is  considerably  greater  when 
the  number  of  steps  per  minute  are  few,  but  commences 
to  diminish  when  the  frequency  of  step  increases,  and 
finally  again  increases.  There  is,  then,  for  each  pace 
an  optimum  rate  of  steps  per  minute,  which  corresponds 
to  the  point  at  which  the  velocity  increases  propor- 
tionately faster  than  energy  is  expended. 

There  are  other  points  to  be  considered  in  choosing 
a  pace.  Energy  must  not  be  exhausted  so  quickly 
that  the  muscles  have  not  time  to  recover  from  the 
effects  of  fatigue.  A  lon^  walk,  in  which  a  £i*eat  deal 
of  energy  has  been  expended,  may  be  borne  with  im- 
punity, while  rapid  running  would  soon  exhaust  the 
muscular  strength,  although  the  total  expenditure  of 
energy  may  be  much  less. 

As  the  studies  just  described  have  only  been  made  in 

If  the  rate  of  step  is  rapid,  a  slight  extension  is  afforded  to  the  oscilla- 
tions by  the  short  duration  assigned  to  it.  Thus,  in  walking,  ilie 
amplitude  of  the  vertical  oscillations  of  the  body  is  related  to  the 
length  of  step ;  it  is  independent  of  the  length  in  running ;  in  fact,  an 
invrrse  relationship  can  almost  be  detected. 

C.  Variation*  in  the  Amount  of  Worl;  don*,  in  the  Arcel V ration  and 
Slowing  of  the  Horizontal  Translation  'of  th^  Boil;/. —  1  his  factor  in  the 
work  increases  fairly  regularly  with  the  rate  and  length  of  the  step. 
In  running,  it  assumes  considerable  proportions,  although  the  absolute 
variations  in  speed  are  slight.  This  is  because  the  gain  or  loss  of  vital 
energy  is  in  proportion  to  the  difference  of  the  squares  of  the  maximum 
and  minimum  velocities  of  translation. 


1H8  MOVEMENT 

a  small  number  of  subjects,  and  those  generally  of 
good  physique,  the  results  cannot  be  generally  applied 
to  the  average  man— to  a  soldier,  for  instance. 

The  officers  in  our  army  have  taken  an  interest  in 
these  researches,  and  have  furnished  us  with  the  means 
of  repeating  them  on  a  considerable  number  of  soldiers. 
The  influence  of  the  figure,  the  weight  of  the  body,  the 
uniform,  and  the  weight  carried,  had  all  to  be  taken 
into   consideration.      With    the    co-operation   of    M. 

Demeny  and  Lieutenant  R ,  we  carried  out  these 

researches,  and  our  first  results  were  reported  to  the 
Minister  of  War. 


CHAPTER  X 

LOCOMOTION   IN   MAN 
From  an  Artistic  Point  of  View 

Summary. — Influence  of  Photography  on  Art— Different  characteristics 
of  ancient  and  modern  works  of  art — Photography  catches  tin- 
real  attitude — Importance  of  representing  the  correct  outline 
of  muscles  during  different  actions— Photographs  taken  from 
different  points  of  view — Photographs  taken  from  above — 
Study  of  the  most  characteristic  attitudes  in  a  movement 
—  importance  of  having  a  series  of  photographs  from  which  to 
cho'  se  the  most  expressive  attitude — Analysis  of  facial  expression 
— Choice  of  the  best  method  for  procuring  artistic  results. 

Photography  has  already  rendered  great  services  to 
Art.  Some  artists  openly  admit  it,  and  many  more 
make  use  of  it,  as  may  readily  be  seen  by  comparing 
recent  works  with  those  of  earlier  date.  It  is  more 
especially  instantaneous  photography  that  has  had 
such  an  influence,  because  it  has  afforded  reliable 
pictures  of  phenomena  of  very  short  duration,  such,  for 
instance,  as  of  sea  waves,  or  even  of  the  attitudes  of 
men  or  animals  during  the  performance  of  the  most 
rapid  movements. 

We  are  not  qualified  to  speak  of  iEsthetics,  still  less 
to  discuss  the  question  as  to  whether  Art  has  the  right 
to  represent  violent  actions,  or  whether  it  should 
restrict  itself  to  more  reposeful  attitudes.  In  the 
latter,  the  characteristic  expressions  are  easier  to 
reproduce  from  living  models ;  but,  as  a  matter  oi  fact, 


170 


MOVEMENT 


it  is  incontestable  that,  in  ancient  times,  as  well  as  at 
the  present  day,  artists  have  often  represented  move- 
ment of  the  most  active  description,  such  as  running  or 
fighting.  Now,  if  old  masterpieces  are  compared  with 
those  of  recent  times,  one  is  struck  with  this  difference 
between  them,  that  the  modern  attitudes  are  quieter 
and  better  poised,  so  to  speak,  while  in  ancient  works 
of  art  the  figures  sometimes  appear  in  positions  of 
unstable  equilibrium.     Fig.  110,  taken  from  a  Greek 


Fig.  110. — Ocydromes  or  swift-runners  (from  a  Greek  vase). 


picture,  is  an  example  of  this  kind.  Every  one  can 
think  of  some  modern  picture  representing  a  similar 
subject.  In  sculpture  especially,  the  action  of  running 
is  differently  represented  nowadays.  The  supporting 
leg  is  generally  seen  vertically  extended  beneath  the 
centre  of  gravity  of  the  body,  while  the  other  leg  is 
in  an  extreme  position  of  elevation  behind. 

Nature  herself  may  fairly  be  appealed  to  in  deciding 
between  these  two  methods  of  representing  the  same 
action.  Instantaneous  photography  is  an  excellent 
means  of  showing  the  actual  attitudes  assumed.     There 


LOCOMOTION   IN   MAX  171 

is  no  doubt  about  the  decision.  Fig.  Ill,  for  instance, 
shows  that  a  man  in  running  assumes  at  certain 
moments  positions  exactly  like  those  represented  in 
the  old  masterpieces.* 


Fig.  111. — Instantaneous  photograph  of  a  runner  :  the  position  of  the  legs  is  the  same 
as  that  of  tlie  man  on  tlie  extreme  left  of  the  toregomg  illustration. 

It  is  quite  easy  to  prove  that  runners  never  appear 
in  the   positions   adopted   by   certain  modern  artists, 

*  One  sometimes  sees  on  a  Greek  vase  a  group  of  runners  in  the 
most  curious  positions.  It  is  a  perfectly  familiar  fact  that  a  man  in 
running  or  walking  always  swings  the  corresponding  arms  and  legs  in 
opposite  directions.  The  corresponding  arm  and  leg  move,  so  to  speak, 
in  diagonal  association.  Now,  on  the  Greek  vase  the  arm  and  leg 
belonging  to  the  same  side  are  represented  as  moving  in  the  same 
directions.  Now,  was  this  style  of  running,  which  is  somewhat 
suggestive  of  the  ambling  of  quadrupeds,  really  practised  on  the 
ancient  race-course  ?  or  is  it  a  mistake  on  the  part  of  the  decorator 
of  the  vase  ?  This  is  a  question  we  are  unable  to  answer.  Such 
a  style  of  running  is  quite  different  from  that  n  >w  practised;  yet 
at  the  same  time  it  does  not  appear  physiologically  impossible.  It  is 
certainly  a  question  worth  considering. 


172  MOVEMENT 

who  seem  to  forget  that  one  of  the  characteristics  of 
running,  and  even  of  walking,  is  to  maintain  a 
continuous  position  of  unstable  equilibrium.  We 
must  not,  however,  spend  time  on  these  reflections, 
for  by  criticizing  the  details  of  works,  which  are 
excellent  in  other  respects,  we  may  expose  ourselves  to 
the  warning,  "Ne  sutor,  ultra  crepidam."  We  will 
only  remark  that  among  the  infinite  variety  of 
attitudes  shown  by  chronophotography  in  registering 
all   the   jihases   of  a   movement,   there   are   certainly 


Fig.  112.— A.  man  walking;  successive  positions  afforded  by  chronophotogiaphy  on 

,    fixed  plates. 

some  which  might  be  accepted  by  artists  without 
transgressing  the  laws  of  aesthetics,  and  an  interesting 
variety  might  be  given  to  such  representations.  Thus, 
in  Fig.  112,  in  which  a  nude  figure  is  represented  as 
walking,  a  series  of  attitudes  is  shown,  amongst  which 
several  could  be  introduced  into  a  work  of  art ;  and  so 
with  many  other  series  of  the  same  kind. 

In  these  pictures  artists  would  also  find  a  faithful 
expression  of  the  action  of  the  muscles,  which  show  the 
conditions  of  contraction  or  relaxation  by  the  degree 
of  prominence.  Now,  these  two  opposite  conditions 
of    the    muscles    are     closely    associated    with    each 


LOCOMOTION   IN  MAN  173 

phase  of  the  movement  in  which  they  take  part.  The 
standing  out  of  muscles  in  action  has,  so  to  speak, 
an  individual  expression,  just  as  is  the  case  with  the 
facial  muscles,  and  if  most  subtle  physiological  know- 
ledge could  be  applied  in  all  cases,  it  might  be  said 
that  the  modelling  of  a  limb  could  not  only  express 
the  action  of  the  time  being,  but  could  suggest  to 
a  certain  extent  its  immediate  successor. 

Some  interesting  experiments  of  M.   Demeny  show 


Fitr.  113.— ChLoiiopliotu^rapLiic  illustration  of  a  runuer. 

that  the  extension  of  an  arm  in  striking,  if  it  is  to  be 
complete,  must  be  accompanied  by  the  total  relaxation 
of  the  flexor  muscles.  The  latter  muscles,  however, 
come  into  play,  if  the  movement  of  extension  is  to  be 
arrested.  As,  for  instance,  in  the  case  of  a  man 
preparing  to  strike,  without  the  actual  intention  of 
delivering  the  blow. 

In  the  four  following  figures,  the  expression  of  the 
outstanding  muscles  varies  according  to  the  nature  of 
the  preceding  movement,  although  the  final  attitude 
13 


174 


MOVEMENT 


of  the  arm  is  the  same.  Thus  Figs.  114  and  115  both 
represent  a  semiflexed  arm,  but  in  the  first  the 
outstanding  biceps  shows  that  a  movement  of  flexion 
is  in  process  of  production,  and  in  the  second  it  is 
the  triceps  (extensor  muscle)  which  stands  out  most 


Fig.  114. — Flexion  of  an  arm. 


Fig.  115. — Extension  of  an  arm. 


markedly,  while  the  biceps  is  flattened.  The  attitude 
here  represented  corresponds  to  a  phase  in  the  extension 
of  the  limb. 

In  alternating  movements,  the  antagonistic  muscles 
come  into  play.     If  extension  of  the  arm   is   to   be 


Fig.  116. — Alternating  movr-men 
and  extension. 


Fig.  11' 


-Single  movement  of  forcible  exten- 
sion (delivery  of  a  blow). 


followed  by  flexion  (Fig.  116),  although  the  triceps 
is  the  muscle  directly  concerned  in  the  movement, 
the  biceps  is  also  contracted,  partly  to  arrest  the 
momentum  of  extension  and  partly  so  as  to  be  ready 


LOCOMOTION  IN  MAN  175 

for  immediate  action.  If  the  blow  is  delivered  in  a 
definite  manner,  as,  for  instance,  a  blow  with  the  fist 
(Fig.  117),  the  moment  the  limb  is  extended  the 
muscles  have  no  more  to  do,  and  so  relax  themselves. 

For  the  purpose  of  sculpture  the  model  should  be 
viewed  from  different  aspects.  By  taking  chrono- 
photographs  of  a  moving  man  from  some  point  above 
his  head  (Fig.  118),  a  horizontal  projection  is  obtained 
which  shows  the  exact  contour  of  the  body.  This 
photograph,  as  well  as  those  taken  from  different 
angles,  would  doubtless  be  very  useful  to  the  sculptor.* 


Fig.  118.— Chronophotograph  of  a  runner  taken  from  above.     (Horizontal  projection.) 

Quite  apart  from  any  artistic  object,  it  is  often 
necessary  to  have  recourse  to  various  forms  of  modelling 
to  represent  the  attitude  of  man,  or  the  movements  of 
animals,  in  the  three  dimensions  of  space.  We  have 
often  utilized  this  method  for  determining  from  several 
photographs,  taken  simultaneously,  the  attitude  of 
a  bird's  body  and  wings  during  the  act  of  flight.  We 
only  wish  that  some  artist  would  devote  his  talents, 

*  It  was  proposed  some  time  ago  to  produce,  under  the  name  of 
photosculpture,  a  method  for  mechanically  reproducing  a  model  of 
an  individual. 

The  person  was  placed  in  the  middle  of  a  circle,  on  the  circumference 
of  which  were  arranged  a  row  of  cameras.  Each  of  these  cameras 
took  at  the  same  moment  a  photograph  of  the  figure  which  was  thus 
represented  from  various  points  of  view.  Each  photograph  was 
enlarged  to  a  convenient  size  and  transferred  to  a  metal  plate  and 
converted  into  a  sort  of  mould.  On  pressing  some  plastic  material 
on  to  the  plate,  a  rough  model  was  obtained,  absolutely  exact  as  far  as 
attitude  was  concerned,  and  one  from  which  the  sculptor  could  execute 
a  properly  finished  copy. 


176  MOVEMENT 

by  the  aid  of  such  photographs,  to  the  representation 


Fig.  119.  -  Statuette  made  from  cbronophotographs 

of  men  in  the  act  of  running  just  at  the  moment  when 
the  feet  come  in  contact  with  the  ground. 


LOCOMOTION   IN   MAN  177 

M.  Engrand,  wishing  to  work  on  these  lines,  made 
the  statuette  represented  in  Fig.  119.  The  attitude  is 
very  different  to  those  usually  presented  in  Art ;  the 
foot  which  touches  the  ground  is  well  in  advance  of 
the  centre  of  gravity,  so  that  the  choice  of  such  an 
attitude  perhaps  creates  a  practical  difficulty,  inas- 
much as  the  figure  is  in  unstable  equilibrium.  In 
order,  however,  to  reconcile  this  with  physiological 
knowledge,  an  attitude  should  be  chosen  in  which 
the  centre  of  gravity  lies  exactly  over  the  point  of 
support.  At  this  moment  the  elevated  leg  is  never 
behind  the  leg  which  supports  the  weight  of  the  body, 
but  lies  directly  across  it.  This  attitude  is  seen  in  all 
human  paces,  in  walking  as  well  as  in  running,  with 
this  difference,  that  in  walking  the  legs  are  much  less 
flexed  at  the  joints. 

Study  of  the  most  Characteristic  Attitudes  in  a  Move- 
ment.— In  representing  a  movement,  for  instance,  one  of 
a  man,  an  artist  rightly  attempts  to  reproduce  a 
phase  which  is  visible  to  the  eye.  It  is  usually  the 
preliminary  or  the  final  phase  which  can  be  best 
appreciated.  AYhen  a  machine  is  in  motion,  there  are 
certain  parts  of  it  which  are  only  visible  when  they 
reach  their  dead  points,  that  is  to  say,  for  the  brief 
moment  when  the  direction  of  movement  is  changed. 
And  this  is  also  the  case  with  certain  movements  in 
man.  Some  attitudes  are  maintained  longer  than 
others.  Now,  chronophotography  on  fixed  plates  could 
be  used  to  determine  these  positions.  They  are 
recognizable  in  the  photograph  as  the  ones  which  have 
left  the  most  intense  impressions  on  the  sensitized 
plate — in  fact,  as  those  which  have  had  the  longest 
exposure.  Thus  in  Fig.  120,  which  represents  a 
fencer  in  the  act  of  lunging,  most  of  the  impressions 
are  indistinct  or  confused,  while  two  of  them  stand  out 
as  well  defined  positions.     The  first  of  these  is  when  the 


178 


MOVEMENT 


LOCOMOTION  IN  MAN  179 

man  is  preparing  for  his  thrust,  and  the  second  is  when 
his  arm  is  extended  to  its  utmost  limit  after  he  has 
executed  the  lunge. 

Fig.  40  was  taken  from  two  equally  good  photographs 
of  a  boxer.* 

In  all  possible  actions,  such  as  pulling  a  string, 
lifting  a  weight,  turning  a  wheel,  pushing  a  wheel- 
barrow, etc.,  there  are  some  attitudes  which  last  longer 
than  others,  and  which  may  be  called  "positions 
of  visibility."  t  Chronophotography  would  determine 
these  with  the  greatest  precision. 

Importance  of  having  a  Series  of  Photographs  from 
which  to  choose  the  most  Expressive  Attitude. — If  a 
movement  had  always  to  be  represented  in  its  slowest 
phase,  Art  would  be  beggared  of  all  originality  of 
expression.  We  should  then  have  a  sort  of  catalogue 
of  stereotyped  attitudes,  just  as  we  have  laws  of 
anatomical  proportion.  Hampered  by  these  limita- 
tions, the  artist  would  lose  all  individuality.  He  ought, 
on  the  contrary,  while  taking  Nature  as  his  model,  to 
make  an  independent  choice  between  the  objects  offered 
to  him.  Among  the  many  photographs  we  have 
obtained,  some  have  struck  us  as  particularly  expres- 
sive, and  we  believe  that  they  are  the  very  ones  that 
an  artist  would  select. 

In  a  series  of  photographs  that  we  took  of  a  man 
striking  a  forcible  blow  with  a  stick,  there  was  one 
that  particularly  appealed  to  us.  At  the  moment  of 
supreme  effort  almost  every  muscle  in  the  body  stood 
out  in  forcible  contraction.  This  would  not  occur 
in  a  quieter  action,  or  in  a  more  limited  movement. 

*  These  two  figures  were  borrowed  from  an  article  on  physical 
exen-ise  bv  M.  Denieny,  illustrated  by  means  of  chronophotography 
(La  Nature,  October  11,  1890> 

t  With  regard  to  the  locomotion  of  quadrupeds,  we  shall  show, 
further,  that  in  the  horse,  for  instance,  these  phases  of  slow  motion 
never  occur  in  all  the  limbs  at  once. 


180  MOVEMENT 

A  slow  action,  such  as  that  of  a  man  sitting  down 
on  the  ground  and  then  stretching  himself  out  in  a 
recumbent  position,  would  present  no  such  general 
muscular  contraction. 

Chronophotography  of  Facial  Expression. — With  the 
camera  which  we  used,  although  it  has  only  one 
objective,  a  subject  can  be  photographed  at  a  near 
distance,  and  show  no  alteration  in  perspective,  how- 
ever long  be  the  series  of  photographs.  It  is  the 
only  kind  which,  up  to  the  present,  has  been  capable 
of  affording  a  series  of  photographs  which  shows  in 
all  their  details  the  changes  in  facial  expression,  the 
various  movements  of  the  hands,  and  the  different 
positions  of  the  feet  in  walking. 

It  would  be  interesting  to  follow  in  this  way  all 
the  transitions  between  a  scarcely  perceptible  smile 
and  a  hearty  laugh,  and  to  catch  the  characteristic 
expressions  of  astonishment,  anger,  and  other  emotions. 
The  great  difficulty  is  to  find  a  subject  capable  of 
giving  these  various  expressions  in  a  perfectly  natural 
manner.  Most  people  would  only  produce  a  grin  or 
a  grimace.  Clever  actors  would  no  doubt  succeed 
better  in  assuming  the  various  emotional  expressions  ; 
and  the  method  might  even  be  useful  to  them  in 
their  own  studies.  But  that  which  is  rendered  to 
perfection  by  chronophotography  is  the  movement 
which  accompanies  the  act  of  articulation.  M.  Demeny 
has  paid  special  attention  to  this  extension  of  our 
method,  and  lie  has  met  with  immense  success.  With 
strong  and  well-directed  light  he  has  shown  the  way 
the  tongue  moves  in  the  articulation  of  consonants. 
His  researches  are  of  value  from  a  phonetic  point  of 
view,  and  practically  it  ought  to  be  of  service  in  the 
teaching  of  deaf  mutes.  One  ingenious  method  for 
instructing  deaf  mutes  consists  in  teaching  them  to  read 
the  various  movements  of  the  lips  in  producing  different 


LOCOMOTION   IN   MAN 


181 


182  MOVEMENT 

words,  and  to  carry  on  a  continuous  conversation  in 
this  way.  M.  Demeny  was  very  anxious  to  know 
whether  deaf  mutes  would  be  able  to  make  out  a 
conversation  carried  on  by  means  of  a  series  of  photo- 
graphs. The  result  of  his  experiment  was  most 
satisfactory.  The  deaf  mutes  read  from  the  chrono- 
photographs  the  words  which  had  been  uttered.  It 
is  unnecessary  here  to  remark  that  without  special 
teaching  this  novel  kind  of  writing  cannot  be 
deciphered.* 

And  now  from  an  artistic  point  of  view.  What  is 
to  be  the  outcome  of  this  new  method  of  reproducing 
the  movements  of  speech?  Painters  have  hitherto 
apparently  paid  no  attention  to  the  subject. 

In  the  most  animated  scenes,  it  is  the  general 
expression  of  the  features  that  conveys  an  idea  of 
what  the  individuals  are  supposed  to  be  saying,  and 
the  same  holds  good  in  sculpture.  Kude  has  twice 
attempted  to  represent,  if  not  actual  words,  at  least 
a  cry  of  imprecation  or  command. 

We  wanted  very  much  to  know  what  sort  of  expres- 
sion a  man's  features  would  assume  when  he  uttered 
a  loud  exclamation.  The  attendant  at  the  Physio- 
logical Station  was  the  subject  of  our  experiment. 
He  was  placed  in  front  of  the  objective,  and  told  to 
shout  at  us  several  times  in  succession  at  the  top  of 
his  voice.  The  series  of  photographs  thus  obtained 
showed  the  periodical  repetition  of  the  facial  expres- 
sion, but  so  curiously  contracted  were  the  muscles 
of  expression  that  the  appearance  was  rather  that  of 
an  ugly  grimace ;  and  yet  simply  to  watch  him  there 
was  nothing  extraordinary  in  the  man's  expression. 

The  peculiarity  of  the  photographs  was  due  to  the 
fact  that  they  caught  exceeding  fleeting  expressions 
of  the   face— movements   which   were  really  ones   of 

*  C.  R.  de  V  Acade'mie  des  Sciences,  t.  cxiii.  p.  216,  1891. 


LOCOMOTION  IN  MAN  183 

gradual  transition,  and  none  of  which  were  seen  as 
isolated  expressions. 

Let  us  place  the  series  of  photographs  in  a  zootrope 
and  watch  them  as  they  pass  in  succession  before  the 
eyes  as  the  instrument  revolves  at  a  convenient  speed. 
All  the  strangeness  then  disappears,  and  we  only  see 
a  man  articulating  in  a  perfectly  natural  way.  What 
does  this  fact  imply  ?  Is  it  not  that  the  ugly  is  only 
the  unknown,  and  that  truth  seen  for  the  first  time 
offends  the  eye  ?  We  are  often  faced  by  this  question 
while  examining  instantaneous  chronophotographs  of 
horses  moving  at  a  great  pace. 

These  positions,  as  revealed  by  Muybridge,  at  first 
appeared  unnatural,  and  the  painters  who  first  dared 
to  imitate  them  astonished  rather  than  charmed  the 
public.  But  by  degrees,  as  they  became  more  familiar, 
the  world  became  reconciled  to  them,  and  they  have 
taught  us  to  discover  attitudes  in  Nature  which  we 
are  unable  to  see  for  ourselves,  and  we  begin  almost 
to  resent  a  slight  mistake  in  the  delineation  of  a 
horse  in  motion.  How  will  this  education  of  the  eye 
end,  and  what  will  be  the  effect  on  Art  ?  The  future 
alone  can  show. 

The  Fall  of  Draperies. — The  arrangement  of  draperies 
played  an  important  part  in  ancient  Art.  In  the 
masterpieces,  whether  of  painting  or  sculpture,  which 
have  been  handed  clown  to  us,  the  folds  in  the 
materials  are  so  conscientiously  represented  that  they 
have  served  as  exact  patterns  of  the  different  Greek 
and  Roman  vestments.  Our  colleague  Heuzey  has 
interested  himself  in  these  questions,  and  has  in- 
augurated a  special  course  at  the  Ecole  des  Beaux  Arts, 
in  which  young  artists  are  taught  how  to  drape  their 
models  correctly  and  gracefully. 

Fig.  121  shows  a  woman  dressed  in  the  Greek  style, 
and   indicating   the  pose  of  the  body  in   an   ancient 


184 


MOVEMENT 


dance.  Fig.  122  shows  the  same  woman  draped  in 
a  cloak,  and  turning  round  in  a  sort  of  valse.  M. 
Maurice  Emmanuel,  who  is  bringing  out  an  important 
work  on  the  dances  of  antiquity,  asked  us  to  take 
instantaneous  photographs  of  certain  attitudes,  such 
as  he  noticed  on  some  of  his  bas-reliefs  and  Greek 
vases.  On  looking  at  these  photographs  one  cannot 
help  recognizing  a  sort  of   general   suggestiveness  of 


Fig.  Li 


of  the  attitudes  of  a  Greek  dance,  at 


the  particular  movement  of  the  dance  by  the  fall  of 
the  drapery. 

Even  the  successive  phases  of  a  dance  may  be 
followed  in  a  series  of  chronophotographs,  but  the 
narrow  limits  of  this  book  only  allow  us  to  offer  a 
few  examples  (Fig.  121). 

It  is  easy  to  see  what  a  variety  of  attitudes  could 
be  obtained  on  a  long  film.      And   these  could  show 


LOCOMOTION   IN   MAN  185 

all  the  phases  of  a  performer's  movements,  and  afford 
the  artist  a  choice  of  more  or  less  expressive  and 
graceful  positions. 

Choice  of  Method  for  obtaining  Artistic  Results. — Both 
kinds  of  chronophotography  answer  excellently  for 
securing  artistic  results.  Figs.  112  and  113,  taken  on  a 
fixed  plate,  are  of  interest,  for  they  clearly  demonstrate 
the  uniform  transition  from  one  attitude  to  another. 
Photographs  taken  on  a  moving  plate  can  be  more 
numerous  for  the  reasons  previously  given  in  Chapter 
VII.,  and  therefore  offer  a  greater  variety  of  attitudes, 
and,  further  than  this,  they  can  be  taken  with  any 
kind  of  background.  And  although  we  have  generally 
adopted  a  black  background,  that  is  only  because  the 
figures  stand  out  more  sharply. 

If  a  light  background  is  used,  some  of  the  outlines 
of  the  figures  stand  out  very  poorly.  In  using  a  dark 
background,  care  must  be  taken  not  to  let  the  light 
fall  exclusively  on  one  aspect  of  the  model,  or  else 
the  parts  in  shadow  may  be  confused  with  the  back- 
ground. On  the  other  hand,  in  using  a  light-coloured 
background,  if  the  model  is  in  lull  sunlight,  violent 
shadows  will  be  thrown  on  to  the  field,  and  look  so 
fantastic  that  it  is  as  well  to  avoid  them.  This  can 
be  done  by  placing  the  background  at  some  distance 
from  the  model  so  that  the  shadow  fails  to  reach  the 
distance,  and  is  lost  in  the  ground.  Skilled  photo- 
graphers have  a  thorough  knowledge  of  the  conditions 
of  light,  and  are  therefore  able  to  photograph  their 
subject  to  the  best  advantage.* 

*  It  is  not  only  the  material  on  which  the  prints  are  obtained  that 
influences  the  artistic  merit  of  the  picture,  the  polish  on  some 
photographs  may  render  the  subject  difficult  to  distiDguish  under 
certain  conditions  of  light.  As  to  reproductions  on  paper,  the  different 
methods  are  of  unequal  merit.  In  typography,  Bimili-gravures  give 
some  of  the  best  effects,  but  they  are  not  so  good  as  those  obtained 
by  proof  impressions  with  thick  ink. 


CHAPTER  XI 

LOCOMOTION   OP   QUADRUPEDS 

Summary. — Chronography  shows  how  the  feet  rise  and  fall  in  the 
d liferent  paces  of  a  horse — Transition  or  passage  from  one  pace 
to  another — Representation  of  the  attitudes  in  all  paces  of  a 
horse,  as  shown  by  chronography  and  hoof-marks — Comparison 
between  diagrams  obtained  by  these  methods  and  those  obtained 
by  instantaneous  photography — Chronophotography  applied  to 
the  representation  of  a  horse  in  motion— Artistic  representation 
of  the  horse  among  the  ancients — Locomotion  of  the  horse  from 
the  physiological  point  of  view — Geometrical  chronophotography 
of  the  movements  taken  as  a  whole— Individual  movements  of  the 
foot  and  fetlock. 

Of  all  four-footed  animals,  the  locomotion  of  the 
horse  is  best  understood.  For  some  time  past 
specialists  have  applied  themselves  to  the  study  of 
equine  paces,  both  regular  and  irregular,  and  have 
attempted  to  define  the  characteristics  of  each  pace, 
according  to  the  sequence  in  which  the  feet  strike  the 
ground ;  but,  as  we  have  already  remarked,  however 
observant  the  human  eye  may  be,  its  scope  is  still  very 
limited.  This  is  proved  by  the  varied  opinions  of 
different  authors  concerning  the  characteristics  and 
mechanism  of  certain  paces  of  the  horse.  The  graphic 
method  has,  however,  in  our  opinion,  been  useful  in 
determining  the  character  of  each  pace  with  great 
exactitude,  and  in  showing  how  the  transition  occurs 
between  one  pace  and  another. 

The  difficulty  of  observing  the  different  paces  con- 
sists in  having  to  follow  the  movements  of  all  four 


LOCOMOTION   OF   QUADRUPEDS  187 

limbs  at  one  and  the  same  moment.  The  question  is, 
however,  largely  simplified,  if  the  quadruped  is 
looked  upon  as  two  bipeds  walking  one  behind  the 
other,  and  presenting  various  combinations  of  steps  ac- 
cording to  the  individual  sequence  of  each.  If  two  men 
take  up  such  positions,  the  one  in  front  will  reproduce 
the  movements  of  the  fore  feet  of  a  horse,  and  the  one 
behind  those  of  the  hind  feet.  Both  will  execute  in  a 
given  time  an  equal  number  of  steps,  but  by  varying 
the  sequence  they  can  imitate  all  the  paces  of  a  horse. 

In  Chapter  I.  we  gave  an  example  of  the  kind  of 
diagram  which  is  used  to  represent  the  successive  rise 
and  fall  of  the  fore  and  hind  limbs  of  a  horse,  whether 
at  an  amble,  a  walk,  a  trot,  or  a  gallop. 

Fig.  123  presents  a  complete  table  of  all  the  paces, 
and  shows  how  one  is  derived  from  another.  In  the 
order  in  which  these  diagrams  are  arranged,  beginning 
from  the  top  in  Fig.  123,  each  differs  from  the  preceding 
one,  inasmuch  as  the  hind  feet  slightly  anticipate 
the  movement  of  the  front.  The  description  under 
these  diagrams  suffices  in  itself  to  show  how  authors 
disagree  in  the  definition  of  each  pace. 

We  only  give  a  brief  account  of  these  chronographic 
researches,  because  we  merely  want  to  give  a  general 
idea  of  the  principles  of  the  method.* 

To  demonstrate  the  value  of  this  method  suffice  it 
to  say  that  these  experiments  have  put  an  end  to  most 
of  the  disagreements  relating  to  equine  paces,  and 
we  believe  that  the  results  of  our  investigations  are 
now  universally  accepted. 

Transition  or  Passage  from  one  Pace  to  Another.— It  is 
very  difficult  for  an  observer  to  realize  how  an  alter- 
ation of  pace  is  effected  ;  chronography  demonstrates 
this  very  clearly.  This  is  one  of  the  greatest  practical 
advantages  of  the  method.     Let  us  compare  the  paces 

*  See,  for  analysis  of  paces,  T.a  Machine  Animate,  pp.  H0-18G. 


188  MOVEMENT 

of  the  two  men  walking  one  behind  the  other.     The 


Fig.  ITS. — Synoptic  chart  of  a  horse's  paces 


No.  2. 


No.  3. 


No.  1.  Ordinary  amble  according  to  all 
authorities. 
Amble  rompu   (racking  amble), 

according  to  Merc  he. 
Pas  releve,  according  to  Bouley 
Ordinary  going  pace  of  a  horse, 

according  to  Mazure. 
Racking     amble,    according     to 
Houley. 

I  Traquenard  (racking  pace),  ac- 
'      cording  to  Lecoq. 
No.  4.  Ordinary  pace,  according  to  Lecoq. 


No. 


according  to  different  authorities 

5.  Ordinary  pace,  according  to  Bouley, 
Vincent  and  Goiffon,  Solleyso), 
Colin. 

6    Ordinary  pace,  according  to  Raabe. 

1.  Loose  trot. 

8.  Ordinary  trot.  (In  the  figure,  it  is 
supposed  that  ihe  animal  trots 
without  ever  leaving  the  ground, 
which  only  rarely  happens.  The 
notation  only  takes  into  con- 
sideration the  rhythm  of  the 
beats. 


steps  more  or  less  alternate  or   correspond,  and   the 


LOCOMOTION   OF    QUADRUPEDS  189 

united  movements  reproduce  the  gait  of  a  quadruped. 
Now,  if  one  of  these  men  for  a  moment  slackens  or 
hurries  up  his  rate  of  walking,  and  then  continues  as 
before,  the  relationship  will  be  changed,  and  the  net 
result  will  be  an  alteration  in  the  quadrupedal  pace. 


Fig.  124. — Transition  from  walking  to  trotting.     Chronographic   record,  read  from 
left  to  right. 

This  is  why  a  soldier,  who  in  marching  has  got  out  of 
step,  gives  a  little  hop  to  regain  the  time. 

We  have  recorded  some  of  these  transitions  by 
means  of  chronography.  Thus  Fig.  124  represents  such 
a  transition  from  walking  to  trotting. 

Independently  of  the   general  acceleration  of  beat, 


Fig.  125. — Transition  from  trotting  to  walk 


this  transition  is  effected  by  an  anticipatory  movement 
on  the  part  of  the  hind  feet,  thus  the  fall  of  the  left 
hind  foot  PG,  which  in  walking  occurred  practically 
during  the  mid  phase  of  rest  of  the  right  fore  foot  AD, 


Fig.  126. — Transition  from  trotting  to  gallop  (three-time:-;. 

gradually  assumes  a  position  less  and  less  in  advance 
of  the   fore  foot,  and   finally  the   two   coincide.     At 
this  movement  a  trotting  step  is  established.    That  the 
14 


190  MOVEMENT 

diagram  may  show  more  clearly  the  gradual  change 
that  occurs  in  the  sequence  of  these  two  diagonal  foot- 
falls, the  lines  which  represent  them  on  the  diagram 
are  united,  so  as  to  mark  the  commencement  of 
each   footfall.      The   connecting-lines,  at  first  widely 


Fig.  127.— Transition  from  a  gallop  (three  time)  to  a  trot. 

separated,  approach  nearer  and  nearer  together,  and 
ultimately  unite  as  the  diagonal  footfalls  become 
perfectly  synchronous,  a  characteristic  of  the  trotting 
step.* 

The  Successive  Positions  of  the  Feet  indicated  by  their 
Impressions  on  the  Ground. — Although  chronography 
may  be  a  perfect  method   for  expressing   the   actual 

*  Other  transitions  have  been  observed  in  the  same  way.  The 
transition  from  trotting  to  walking  is  effected  by  an  inverse  procedure 
to  that  which  has  just  been  described.  It  is  brought  about  by  the 
gradual  hurrying  up  of  the  movements  of  the  fore  feet,  and  this 
is  accompanied  by  a  general  slackening  in  speed  (Fig.  125).  The 
dotted  line  uniting  the  diagonal  beats  of  the  left  feet,  is  at  first 
vertical,  and  expresses  that  in  trotting  these  beats  are  simultaneous 
This  line  becomes  more  and  more  oblique  during  the  process  of 
transition,  and  thus  shows  how  the  synchronism  ceases,  and  that  there 
is  a  delay  on  the  part  of  the  hind  feet. 

The  transition  from  trotting  to  galloping  is  very  curious.  Fig.  126  at 
the  commencement  shows  that  the  trot  is  already  rather  broken,  the 
dotted  lines  uniting  the  diagonal  beats  AG-PD  is  at  the  start  rather 
oblique,  and  indicates  a  slight  delay  on  the  part  of  the  hind  foot. 
This  obliquity  increases,  but  only  in  the  left  diagonal  beats.  The 
right  diagonal  pair,  AD-PG,  remain  synchronous,  before  and  after  a 
galloping  pace  has  been  established.  This  transition  is  not  effected 
by  the  delay  of  the  hind  foot  alone,  but  also  by  the  advance  of  the 
fore  foot,  so  that  the  two  diagonal  beats,  which  in  trotting  were 
synchronous,  now  have  an  interval  between  them  equal  to  the  whole 
galloping  step.  This  interval  corresponds  to  the  long  period  of  silence 
noticed  in  ordinary  galloping. 

The  transition  from  galloping  to  trotting  is  effected  by  an  inverse 
process  (Fig.  1^7).  The  transition  from  a  gallop  in  four-time  to  a 
gallop  in  three-time  is  effected  by  a  gradual  anticipation  in  the  beats 
of  the  hind  feet. 


LOCOMOTION   OF   QUADRUPEDS 


191 


sequence  in  which  horses'  feet  strike  the  ground,  it 
gives  no  information  as  to  the  position  on  the  ground 
struck  by  the  feet. 


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Ordinary         Walk  Quuk        Amble.       Jog-trot.         Gallop. 

walk.  '    {long  stride),    walk. 
Fig.  128.— Table  of  the  track  of  ahorse  performing  different  paces. 

The  tracks  or  footprints  left  on  the  ground  by  the 
horse  give  this  information  in  an  exact  manner.     The 


192  MOVEMENT 

tracks  have  been  carefully  studied  in  equitation. 
Horses  have  been  shod  with  different-shaped  shoes,  so 
that  each  hoof  might  leave  on  the  ground  a  mark 
that  could  be  recognized.  Fig.  128,  compiled  from 
diagrams  borrowed  from  different  sources,  shows  the 
corresponding  tracks  of  the  different  paces  of  a 
horse.* 

In  the  track  left  by  the  feet  at  a  walking  pace,  the 
hind  feet  are  placed  in  the  impressions  left  by  the 
front,  the  right  hoof-marks  exactly  alternate  with  those 
of  the  left  feet.  The  distance  between  two  impressions 
on  the  same  side  is  practically  equal  to  the  height  of 
the  horse  at  the  withers.! 

The  hoof-marks  are  not  exactly  superimposed  in 
walking  except  when  the  ground  is  level,  and  the 
animal  moves  at  a  certain  rate.  Going  uphill,  the 
marks  of  the  hind  feet  are  generally  behind  those  of 
the  fore  feet.  They  may  reach  beyond  them  in  walk- 
ing downhill,  with  a  result  rather  like  that  of  ambling. 
In  the  hoof-marks  left  by  a  horse  at  an  amble,  the 
impressions  of  the  hoofs  on  the  same  side  are  not  super- 
imposed. The  marks  of  the  hind  feet  are  far  in 
advance  of  those  of  the  fore  feet. 

The  hoof-marks  left  in  trotting  resemble  those  of 
walking,  except  that  there  is  a  longer  interval  between 
the  steps.     However,  in  slow  trotting,  the  hoof-marks 

*  In  this  table  the  prints  of  the  right  and  left  feet  can  be  recognized 
from  their  position  on  the  riicht  or  left  of  the  dotted  and  parallel  lines. 
The  impression  left  by  a  fore  foot  is  that  of  an  ordinary  horse's  hoof, 
that  by  a  hind  foot  has  two  little  cross-bars  at  the  heel.  The  double 
impression,  that  is  to  say,  when  the  hind  foot  occupies  the  place 
vacated  by  the  fore  foot,  shares  both  thc.se  characteristics,  but  has  only 
one  cross-bar. 

t  Raabe  held  that  there  was  a  constant  and  absolute  equality 
between  the  height  of  ;i  horse  and  the  distance  between  two  consecu- 
tive hoof-marks.  Most  specialists  question  so  exact  a  relationship. 
In  any  case  it  could  only  obtain  in  certain  steady  paces;  horses,  like 
human  beings,  lengthen  their  stride  as  the  pace  is  accelerated  (see 
chap  viii.,  p.  132). 


LOCOMOTION  OF  QUADRUPEDS 


193 


are  not  superimposed,  and  the  hind  foot  does  not  reach 
the  impression  of  the  fore  foot.* 

Representations  of  the  Attitudes  assumed  by  a  Horse 
in  its  Different  Paces  as  shown  by  Chronography  and  the 
Footprints. — It  ought  to  be  possible,  by  combining 
the  two   ideas   of  time  and   space   which  we  already 


Fig.  129.— Representation  of  a  walking  horse,  designed  from  a  chronographic  chart 
and  from  the  footprints. 

know,  to  represent  with  accuracy  the  attitude  of  a  horse 
at  any  given  moment  during  one  of  its  paces.  Vincent 
and  Groiffon  were  also  of  this  opinion ;  their  remarkable 
book  on  the  subject  was  designed  as  much  for  artists 


*  These  tables  are  taken  from  a  treatise  on  the  subject  by  Vincent 
and  Goiffon;  those  of  galloping  are  borrowed  from  Curnieu,  the  latter 
are  reduced  to  a  smaller  scale,  so  that  one  line  may  contain  three 
complete  steps  of  a  gallop.  To  make  the  sequence  in  beat  intel- 
lig  ble,  the  impressions  of  the  feet  which  strike  the  ground  simul- 
taneously are  united  by  a  diagonal  and  dotted  line. 


LOCOMOTION   OF   QUADRUPEDS 


195 


as  for  horsemen.  With 
the  accurate  know- 
ledge afforded  by 
chronography,  which 
reveals  the  exact  phases 
of  rest  or  motion  of 
each  of  the  legs  of  a 
horse,  combined  with 
the  knowledge  afforded 
by  the  hoof-marks,  we 
possess  all  the  data 
necessary  for  construct- 
ing a  perfectly  accu- 
rate representation. 

An  artist  familiar 
with  equine  paces  could 
easily  give  a  fairly 
correct  attitude  of  an 
animal,  but  very  often 
the  representation  de- 
viates considerably 
from  the  reality.  This 
is  what  has  been 
proved  by  instan- 
taneous photography 
of  equine  paces. 

To  prove  satisfac- 
torily that  chrono- 
graphy combined  with 
the  measurement  of 
the  hoof- marks  is  not 
sufficient  for  the  deter- 
mination of  the  real 
attitudes  of  the  horse, 
we  will  give  an  ex- 
ample in  the  form  of 


Fig.  131.— H^rse  walking- 


196  MOVEMENT 

two  illustrations.  Firstly  (Fig.  130),  the  attitude  as 
drawn  from  graphic  analysis  ;  *  secondly  (Fig.  132),  the 
same  as  taken  from  photographs  by  Muybridge.  This 
comparison  is  not  to  the  advantage  of  the  first  diagram, 
in  which  it  may  be  seen  that  the  positions  of  the  elevated 
feet  are  in  some  ways  very  unnatural.  These  dis- 
crepancies occur  almost  exclusively  when  an  attempt 
is  made  to  represent  galloping,  for  in  this  pace  the 
diagrams  constructed  from  chronographic  data  alone 
are  particularly  at  fault. 

Chronography  as  applied  to  the  Representation  of  the 
Horse  in  Motion. —Everybody  is  familiar  with  Muy- 
bridge's  beautiful  photographs,  to  which  we  have  just 
alluded.  They  have  furnished  exact  evidence  concern- 
ing the  movements  of  horses.  Since  instantaneous 
photography  has  become  so  universal,  there  have  been 
published  a  considerable  number  of  magnificent  photo- 
graphs, of  which  artists  have  made  advantageous  use  ; 
but  the  photographs  taken  in  series  are  undoubtedly 
the  most  instructive,  as  far  as  the  sequence  of  the  move- 
ments is  concerned. 

Considerable  advantage  accrues  from  the  application 
of  our  chronophotographic  method  to  researches  of  this 
kind.  More  portable  than  other  cameras,  ours  is  easily 
carried  about,  whatever  be  the  field  of  operations.  It 
gives  the  shortest  exposure,  and  therefore  the  clearest 
images.  We  have  obtained  on  moving  films  some 
extremely  long  series,  which  the  restricted  size  of  this 
book  does  not  permit  us  to  reproduce  in  toto. 

Fig.  131  shows  a  horse  at  a  walking  pace.  The 
fragment  here  given  only  represents  five  consecutive 
images  out  of  a  total  of  twelve,  which  comprise  one 
entire  step,  as  measured  from  the  moment  the  left  hind 


*  These  diagrams  are   taken  from   La  Machine  Animale.     Paris, 
G.  Bailliere,  1873. 


LOCOMOTION   OF   QUADRUPEDS 


197 


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198  MOVEMENT 

foot  reaches  the  ground  till  the  same  foot  completes 
another  step. 

These  images,  when  enlarged  (Figs.  133  and  134), 
gain  in  clearness  what  they  lose  in  detail.  This  is  one 
of  the  disadvantages  of  this  method  of  reproduction 
which  is  required  in  typography,  but  in  impressions 


Fig.  133.— Horse  walking  (enlarged). 

with  thick  ink  the  enlarged  images  still  retain  the 
detail.*  Only  three  characteristic  photographs  of  a 
galloping  horse  are  represented  in  one  series,  and 
these  correspond  to  the  three  beats  of  the  movement, 
namely,  the  first,  second,  and  third.  The  transitions 
and  the  changes  of  foot  produce  very  elegant  attitudes 

*  We  propose,  in  V  Atlas  de  Physiologie  artidique,  to  give  a  few 
series  of  photographs  of  the  horse  in  its  various  paces. 


LOCOMOTION   OF   QUADRUPEDS  199 

(Figs.  136  and  137),  among  which,  no  doubt,  artists 
will  find  some  of  which  they  can  make  good  use. 

The  Uses  of  Photography  in  showing  Marked  Charac- 
teristics in  the  Forms  of  Animals. — In  artistic  repre- 
sentations, correctness  of  attitude  is  not  all  that  is 
required.     To  this  must  be  added  correctness  of  form, 


Fig.  134. — Horse  walking  (enlarged). 

without  which  a  movement  cannot  be  successfully 
represented.  Artists  of  remote  antiquity  appear  to 
have  acquired  a  knowledge  of  some  of  the  paces,  if  not 
of  the  most  complicated  one,  namely,  that  of  walking. 
On  looking  at  Figs.  138  and  139,  examples  of  an  ambling 
pace  will  be  seen  accurately  represented.*     It  is  of  all 

*  These  and  most  of  the  following  figures  have  been  borrowed  from 
the  Duhousset  collection.     They  appeared  in  La  Nature. 


200  MOVEMENT 

paces    the    easiest    to    observe    on     account    of    the 


Fig.  135. — Horse  at  a  canter.     The  series  must  be  read  from  below  upwards. 

symmetry  of  movement;    it    is  what  is   observed   in 
the  case  of  the  ordinary  gait  of  large  animals,  such  as 


LOCOMOTION   OF   QUADRUPEDS 


201 


camels  and  elephants ;  but  beyond  the  accuracy  with 
which  the  attitudes  of  the  limbs  are  rendered,  the  execu- 
tion otherwise  is  heavy,  and  the  perfect  synchronism  of 
movement  on  the  part  of  the  two  horses  in  the  bas- 
relief  of  Hedynet-Abou  looks  very  ridiculous. 

Yet  more  massive  and  unnatural  is  the  horse  repre- 
sented at  a  walking  pace  in  Fig.  140,  but  it  shows  that 


Ftg.  136.— Transition  from  trot  to  gallop. 

in  Assyrian  art  there  was  even  in  those  days  a  con- 
siderable knowledge  of  the  movements  of  a  horse,  for 
the  walk  is,  as  we  said,  the  most  difficult  pace  to  un- 
derstand, and  the  one  most  often  incorrectly  drawn. 

In  ancient  art,  however,  we  sometimes  meet  with 
very  correct  ideas  regarding  this  pace.  First  we  have 
(Fig.  141)  a  bas-relief  of  the  Volscian  period  ;  then  two 


202  MOVEMENT 

figures  on  Trajan's  column,  a  horse  and  rider  (Fig.  142)  ; 
and  a  pack-mule  (Fig.  143). 

Trotting,  which  is  so  often  represented  in  modern 
works,  seems  rarely  to  figure  in  that  of  the  ancients. 

Albert  Durer  sometimes  gave  an  example  of  it,  as 


Fig.  137.— Changing  step  in  a  gallop. 


shown  in  Fig.  144.     Then  there  is  the  classical  horse 
of  Henry  IV.  on  the  Pont-Neuf  (Fig.  145). 

As  for  galloping,  it  is,  perhaps,  the  most  familiar 
pace  in  Greek  art.  The  Parthenon  frieze  offers 
numerous  examples  of  it.  But  there  is  little  variety 
in  the  particular  phase  chosen  by  the  school  of  Phidias 
to  represent  the  movement.  It  is  nearly  always  the 
first  beat  of  the  gallop  which  is  represented,  that  is  to 


LOCOMOTION   OF   QUADKUPEDS 


203 


say,  the  moment  when  the  horse  is  supported  by  one 
hind  foot. 

Fig.  146,  taken  from  a  fragment  of  the  frieze  still  in 


liWIIIlB 

Kill!! 


Fig.  138.— Assyrian  bas-relief.    Horse  at  an  amble  (P.ritisb  Museum). 


Fig.  139.— Kgyptian  bas-relief  (Medynet-Abou).     Two  harnessed  horses  moving  at 
an  amble. 

position  at  the  Acropolis,  represents  an  example  of  this 
kind.      All  these  figures  differ   very  much  from  the 


204 


MOVEMENT 


rapid  galloping  we  are  accustomed  to  see  represented 
in  modern  works.  The  Parthenon  horses  seem  to 
make   no   advance,    although    they    go    through    the 


Fig.  140.  — Assyrian  bas-relief  (Ninive)  horse  walking. 


Fig.   141.— Bas-relief  on  burnt  clay  Volscian   period  (Velletri).     Tbree   harnessed 
horses  walking. 

movements  of  galloping  ;  or,  if  they  appear  to  move  at 
all,  at  nothing  more  than  a  processional  pace. 


LOCOMOTION   OF  QUADRUPEDS 


205 


Locomotion  of  the  Horse  from  the  Physiological  Point 
of  View. — Art  and  Science  join  hands  in  searching  after 


Fig.  142.— Cavalier  at  walking  pace  (Tr.gan's  column). 


Fig   143. — Mule  walking  (Trajan's  column). 

truth.      The    same   methods  serve    equally   well    for 
15 


206  MOVEMENT 

determining  the  various  attitudes  in  which  an  artist 


Fig.  144.— The  Horse  of  Death,  by  Albert  Durer.     The  horse  is  at  a  slow  trot. 


Fig.  145.—  Statue  of  Henry  IV.  on  the  Pont-Neuf.     Horse  at  a  trot. 

should  represent  a  horse,  and  for  following  the  phases 


LOCOMOTION   OF   QUADRUPEDS 


207 


of  its  movements  from  a  physiological  or  mechanical 
aspect.  We  have  applied  the  method  of  geometrical 
chrono-photography  to  the  study  of  equine  paces,  so  as 
to  obtain  a  large  number  of  photographs  on  a  fixed  plate 
in  series,  and  to  show  the  movements  of  each  of  the 
segments  of  the  limbs ;  in  fact,  just  as  we  did  in  the 
case  of  human  movements.  It  would  be  very  difficult 
to  cover  a  horse  with  black  velvet,  and  to  arrange  on  it 
black  spots  and  lines  marking  the  different  joints  and 
the  various  axes   of  the   long  bones.     We,  therefore, 


Fig.  146. — Frieze  at  the  Parthenon.     Horse  at  a  canter. 

chose  an  animal  with  a  dark  coat,  and  in  places  we 
deepened  the  colour  by  painting  it  with  lamp-black. 
Then,  on  the  principal  joints,  we  fixed  little  pieces  of 
white  paper,  the  shape  being  different  for  each  joint — 
one  square,  another  triangular,  another  straight,  and 
another  circular,  and  so  on  (Fig.  147).  The  animal  was 
then  made  to  pass  in  front  of  a  dark  screen,  and  a 
series  of  trajectories  of  the  joints  was  thus  obtained. 
In  the  enlarged  photograph,  the  different  joints  had  to 
be  connected  by  lines,  so  as  to  indicate  the  positions  of 


208  MOVEMENT 

the  skeletal  bones.  This  was  a  troublesome  task,  on 
account  of  the  number  of  joints,  and  because  tLe  images 
of  the  hind-quarters  were  superimposed  in  those  of  the 
fore-quarters.  With  the  assistance  of  Dr.  Pages,  we 
have  constructed  diagrams  of  the  movement  of  horses 
at  different  paces,  although  the  individual  trajectories 
of  the  various  parts  are  occasionally  rather  complicated 
(Fig.  148). 

In  galloping,  chronophotography  demonstrates  very 


Fig.  147.— Horse  prepared    lor  experiments  with  geometrical  chroiiophotograpas. 

strikingly  the  part  played  by  the  elastic  flexor  tendon 
in  breaking  the  shock  of  the  hind  foot  as  it  strikes  the 
ground,  for  at  this  moment  the  foot  supports  the  entire 
weight  of  the  body. 

One  of  our  figures  shows  that  the  fetlock  executes  an 
alternating  movement.  The  extent  of  this  retrograde 
movement  at  the  moment  of  contact  is  very  consider- 
able in  long-limbed  horses.  This  explains  the  easiness 
of  their   action.     All   this    shows   the   advantages  of 


210  MOVEMENT 

geometrical  photographs  for  solving  a  number  of 
technical  questions  relating  to  equitation.  But  it  is  a 
subject  which  in  our  eyes  possesses  a  peculiar  interest, 
for  by  it  we  learn  how  an  animal's  paces  are  affected  by 
the  shape  of  its  limbs.  This  knowledge  is  absolutely 
necessary  for  the  study  of  comparative  anatomy,  for  it 
explains  the  real  significance  of  the  various  shapes  of 
the  bones  and  muscles. 


CHAPTER  XII 

LOCOMOTION"    IN    WATER 

Summary. — Different  types  of  locomotion  in  water — Method  of  photo- 
graphing aquatic  animals — Jelly  fish  :  Comatulre — Locomotion 
by  means  of  undulatory  and  lateral  movements;  the  eel--best 
arrangement  for  studying  its  movements — Locomotion  by  means 
of  undulatory  and  vertical  movements;  the  skate — special 
arrangement  for  studying  its  vertical  undulations  from  different 
points  of  view — Undulatory  movements  of  the  skate  as  seen  from 
the  side:  ditto  as  seen  from  in  front — Tne  sea-horse:  the  fresh- 
water tortoise  — Slow  movements  of  star-fish — Locomotion  of  small 
marine  animals. 

Different  Types  of  Locomotion  in  Water. — Terrestrial 
animals  make  use  of  the  ground  as  a  fulcrum  or  fixed 
point  of  support,  and  their  various  kinds  of  locomotion 
depend  on  the  following  mechanism  :  A  more  or  less 
sudden  effort  on  the  part  of  the  limbs  tends  to  repel 
the  ground  in  one  direction,  and  the  body  in  the  other. 
Now,  since  the  ground  offers  almost  absolute  resistance, 
the  whole  effect  of  the  muscular  effort  is  expended  on 
the  body  of  the  animal. 

The  locomotion  of  aquatic  animals  is  quite  different, 
with  them  the  fulcrum,  or  point  of  support,  is  a  dis- 
placeable  liquid,  and  hence  more  or  less  of  the  muscular 
energy  is  expended  on  useless  work. 

The  various  kinds  of  propellers  which  men  think 
they  have  invented  for  the  purposes  of  navigation,  such 
as  sails,  oars,  and  sculls,  are  represented  in  the  highest 
degree  of  perfection  in  the  locomotor  organs  of  aquatic 


212  MOVEMENT 

animals.  If  the  rotatory  motion  of  the  screw  plays 
no  part  in  organic  nature,  there  are  at  least  certain 
undulatory  movements  of  the  body  or  tail  of  certain 
animals,  which,  from  a  functional  point  of  view,  are 
entirely  analogous  to  those  of  a  screw. 

In  addition,  aquatic  animals  have  other  means  of 
propulsion,  the  like  of  which  men  have  never  made 
use  of,  and  which  might  perhaps  be  tried  with 
advantage. 

Without  attempting  to  offer  a  complete  list  of  the 
various  modes  of  progression  represented  among  aquatic 
animals,  the  following  may  be  enumerated. 

Progression  by  the  force  of  reaction  — animals  which 
project  a  stream  of  water :  jelly-fish,  octopuses,  larvae 
of  certain  insects,  bivalve  molluscs. 

Progression  by  means  of  certain  organs  which  meet 
with  unequal  resistance  in  the  two  phases  of  movement : 
comatulae,  crustaceans,  etc. 

Progression  by  means  of  an  undulatory  movement, 
propagated  along  the  body  in  a  direction  opposed  to 
that  pursued  by  the  animal :  eels,  long-bodied  fish. 

Progression  by  means  of  alternate  shocks  from  a 
flexible  paddle :  aplysia,  carinaria,  and  most  fishes 
possessed  of  a  caudal  fin. 

The  possession  of  an  aquarium  facilitates  the  study 
of  aquatic  locomotion.  But,  as  in  the  case  of  all  other 
animal  movements,  the  eye  is  frequently  unable  to 
follow  manoeuvres  so  rapid  and  complicated. 

The  following  are  the  fruits  of  our  first  attempt  to 
apply  chronophotography  to  the  elucidation  of  this 
subject,  concerning  which  at  present  so  little  is  known. 
Methol  of  taking  Photographs  of  Aquatic  Animals. — 
The  methods  vary  very  much  according  to  circum- 
stances. In  the  simplest  cases,  the  object-glass  is 
directed  towards  an  aquarium  provided  with  glass  sides, 
and  let  into  the  outside  wall  of  a  room  (Fig.   149). 


LOCOMOTION  IN   WATER 


213 


214  MOVEMENT 

Sometimes  a  white  cloth,  set  at  an  oblique  angle,  serves 
as  a  reflector  and  luminous  background,  against  which 
the  animals  are  silhouetted. 

A  series  of  photographs  are  taken  on  moving  films, 
to  show  the  successive  attitudes  corresponding  to  the 
phases  of  movement.  The  chief  difficulty  consists  in 
compelling  the  animal  to  move  in  a  limited  space,  so 
as  not  to  leave  the  prescribed  area  of  the  photographic 
plate. 

Four  lines  are  traced  on  the  walls  of  the  aquarium, 
so  as  to  form  a  rectangular  space  on  which  to  focus. 
The  observer  then  watches  till  the  animal  crosses  this 
space,  and  although  the  transit  may  occupy  only  a 
fraction  of  a  second,  a  series  of  from  ten  to  twenty 
photographs  can  easily  be  taken  in  the  time.  This 
will  be  quite  sufficient  to  show  the  j^hases  of  the 
movement.* 

Jelly-fish  are  fairly  easy  to  study,  owing  to  the 
transparency  of  their  tissues ;  and  some  of  the  details 
of  their  internal  structure  can  be  seen  silhouetted  in 
the  photograph  (Fig.  150). 

By  means  of  a  rod  introduced  into  the  aquarium, 
a  jelly-fish  can  be  brought  into  the  field  of  the  object- 
glass.  The  alternate  contractions  and  relaxations  of 
its  bell  may  be  noticed,  each  of  which  operations 
displaces  a  certain  amount  of  water,  and,  by  means  of 
the  reactionary  impulse,  the  animal  is  propelled  in  an 
opposite  direction.  If  a  jelly-fish  takes  up  a  vertical 
position,  the  direction  of  progression  is  from  below 
upwards,  and  the  animal  rises  in  the  water ;  if  it  is 
horizontally  inclined,  the  direction  of  progression  is  in 
a  corresponding  direction. 

The  locomotion  of  a  comatula  is  exceedingly  curious. 
It  is  usually  found  fixed  on  some  solid  support  like 

*  The  size  of  the  page  being  too  small  for  such  a  long  series  we 
can  only  give  incomplete  specimens  of  these  photographs. 


LOCOMOTION  IN  WATER 


215 


a  flower  by  its  stern,  and  there  it  executes  movements 
which  are  so  slow  that  they  almost  escape  observation. 
But  if  separated  from  its  attachment,  and  irritated  by 
means  of  a  rod,  it  soon  begins  to  throw  its  arms  about 
in  a  rapid  manner — movements  which  result  in  its 
removal  from  the  unwelcome  object.  As  in  the  case 
of  the  jelly-fish,  the  direction  of  movement  corresponds 
to  the  long  axis  of  the  body ;  by  inclining  its  cup 


Fig.  150.— Movements  of  the  bell  of  a  medu«a.  The  first  position  is  the  first  of  the 
upper  series  on  the  right ;  the  last  position  is  the  one  on  the  extreme  left  of  the 
lower  series. 


obliquely,  it  can  alter  the  direction  of  progress.  In 
the  case  here  represented  (Fig.  151),  the  animal  was 
trying  to  rise  from  the  bottom  of  the  aquarium. 

The  following  is  the  method  of  propulsion.  The 
arms  of  a  comatula  are  ten  in  number,  five  invariably 
move  upwards,  and  five  downwards ;  two  neighbour- 
ing arms  never  move  in  the  same  direction.  Those 
which  rise  upwards  approach  the  axis   of  the   body, 


216 


MOVEMENT 


£'£& 


those  which  descend  recede  from  it.     Sometimes  in  the 

phase  of  upward 
movement,  the  fine 
processes  on  the  arm 
can  be  seen  flattened 
lown  against  it  by 
the  resistance  of  the 
water.  In  the  phase 
of  downward  move- 
ment, the  same  pro- 
cesses are  separated 
out,  become  visible, 
and  meet  with  re- 
sistance from  the 
water,  which  thus 
acts,  as  it  were,  as 
a  fulcrum  to  assist 
the  animal  in  its 
locomotion. 

Locomotion  by 
means  of  Undulatory 
and  Lateral  Move- 
ments :  Eels. — Eels, 
and  fishes  of  a  simi- 
lar shape,  progress 
in  a  horizontal 
direction  by  means 
of  an  undulatory 
motion  of  their 
bodies.  To  observe 
this  movement  satis- 
factorily, the  ob- 
server should  place 
"'  himself  above  the 
animal :    a    special 

kind    of    aquarium    is    required    for    taking    chrono- 

photographs. 


Fir..    151.— Cnmatula    executing    movement1 
bottom  of  the  aquarium.    The  series  must  be  read 
from  below  upwards. 


LOCOMOTION  IN  WATER  217 

Special  Arrangement  for  Studying  this  Movement. — 
The  light  should  come  from  below ;  in  fact,  the 
arrangement  shown  in  Fig.  51,  Chap.  V.,  answers  very 
well  for  these  researches.  The  eel  is  silhouetted 
against  the  luminous  background,  and  the  object-glass 
of  the  apparatus  is  directed  vertically  downwards,  or 
else  a  silvered  mirror,  inclined  obliquely  at  an  angle  of 
45°,  reflects  the  image  of  the  fish  towards  the  object- 
glass,  which  is  then  set  horizontally. 

Fig.  152  represents  a  series  of  photographs  in  which 
the  progression  of  the  animal  can  be  followed,  as  well 


Fig.  152.— Eel  moving  in  a  horizontal  plane.  The  horizontal  line  oo  enables  the 
reader  to  appreciate  the  degree  of  obliquity  of  the  lines  which  join  the  veniral  and 
n<dal  portions  of  the  curves  into  which  the  body  is  thrown.  The  degree  of  velocity 
of  progression  is  expressed  by  the  obliquity  of  the  line  aa. 

as  the  undulatory  movements  along  its  body.  The 
oblique  lines  indicate  the  propagation  of  these  waves 
in  relation  to  the  horizontal  line  oo  with  which  the 
head  of  the  animal  would  be  on  a  level  in  the  entire 
series  were  it  not  for  the  progress  made.  The  line  aa, 
obliquely  inclined,  shows  in  each  instance  how  far  the 
eel  has  advanced.  This  line  is  straight,  and  conse- 
quently proves  that  the  velocity  is  uniform.  In 
the  fifth  image,  i.e.  at  the  end  of  half  a  second,  the  eel 
has  advanced  a  distance  equal  to  a  quarter  of  its  own 
length,  say  about  0*075  metres,  which  corresponds 
to  a  rate   of  0*15  metres  per  second.     Further,  the 


218  MOVEMENT 

lines  j)1,jP...nl,n2...9  which  unite  the  ventral  and  nodal 
portions  of  the  same  wave,  express,  by  their  degree  of 
obliquity  with  respect  to  oo,  the  velocity  of  each. 

Actual  measurement  shows  that  the  velocity  of  the 
waves  is  greater  than  the  rate  of  progress  of  the 
animal,  and  that  they  travel  in  an  opposite  direction. 
There  must  be,  therefore,  a  recoil,  as  in  the  case  of 
the  screw  of  a  steamer,  and  it  is  due  to  the  mobility 
of  the  resisting-point. 

Thus,  the  direction  of  movement  of  these  undulations 
in  an  eel,  as  it  moves  forward,  are  directed  from  the 
head  towards  the  tail.  We  believe  that  these  fish, 
when  they  want  to  move  backwards,  reverse  the  direction 
of  these  undulatory  movements,  namely,  that  the  wave 
travels  from  the  tail  towards  the  head.  But  this 
phenomenon  is  difficult  to  produce,  and  we  have  not 
yet  been  able  to  prove  it  by  chronophotography. 
We  studied  in  the  same  way  the  locomotion  of  various 
kinds  of  snakes,  both  terrestrial  and  aquatic;  the 
crawling  of  the  former  and  the  swimming  of  the  latter 
are  very  similar  to  the  movement  of  an  eel,  but  we 
could  not  observe  the  same  regularity  of  motion. 

Locomotion  by  means  of  Vertical  and  Undulatory 
Movements  :  the  Skate. — The  skate,  like  an  eel,  pro- 
gresses by  means  of  undulatory  movements,  but  the 
wave  is  produced  symmetrically  by  the  animal's  twro 
fins.  The  movement  is  in  a  vertical  direction.  To 
photograph  this  movement  the  animal  must  be  viewed 
from  the  side ;  an  aquarium,  as  before  described,  is 
suitable  for  this  purpose.  The  difficulty  which  arises 
in  this  experiment  is  that  of  keeping  the  fish  in  a 
convenient  position,  so  as  to  show7  its  movements  clearly. 
Left  to  itself  in  an  aquarium,  the  skate  remains 
motionless  at  the  bottom ;  yet  if  disturbed  it  swims 
to  the  surface,  and  causes  a  disturbance  of  the  water 
by  flapping  its  fins,  and  it  is  but  seldom  that  it  swims 


LOCOMOTION  IN   WATER  219 

quietly  in  a  forward  direction.  To  keep  a  skate  within 
the  field  of  the  object-glass,  and  to  make  it  execute 
its  proper  movements  of  natation,  we  finally,  after 
various  attempts,  settled  on  a  method  which  answered 
admirably. 

Special  Arrangement  for  studying  the  Vertical  Un- 
dulations from  Different  Points  of  View. — Fig.  153  shows 
an  apparatus  for  holding  the  animal.  A  flat  strip  of 
iron  has  its  two  ends  bent  at  right  angles ;  holes  are 
bored  in  corresponding  positions  in  the  two  uprights, 
and  two  iron  wires  are  passed  through  them,  and 
tightlv  stretched.     On  these  two  wires  two  akss  tubes 


Fig.  153.— The  skate.    Method  of  fixing  the  animal  when  observing  the  movements 
of  its  fins. 

are  threaded,  and  united  by  cross-bars.  The  latter  are 
provided  with  clips  for  holding  the  fish.  One  of  the 
tubes  is  fitted  with  a  toothed  forceps  for  holding  the 
front  part  of  the  fish  ;  the  other  is  provided  with  a  plate 
on  which  the  tail  end  rests,  and  to  which  it  is  fastened 
by  means  of  a  ligature. 

The  fish  is  then  held  immovable  between  these  two 
points  of  attachment ;  the  latter  are  more  or  less 
widely  separated,  according  to  the  length  of  the  fish. 
The  iron  plate  rests  at  the  bottom  of  the  aquarium, 
and  the  object-glass  is  focussed  on  the  fish. 

The  skate  thus  held  in  position  can  neither  advance 
nor  recede,  but  it  can  use  its  lateral  fins  as  much  as 
it  chooses ;  nevertheless,  it  seldom  takes  advantage  of 


220 


MOVEMENT 


this  liberty,  and  only  moves  them  when  irritated.  We 
have  found  the  most  successful  way  of  doing  this  is  to 
scratch  it  beneath  the  tail  with  a  piece  of  stick.     A 

curious  result  fol- 
lows :  an  undulatory 
movement  of  the  fins 
is  propagated  down 
the  length  of  the 
body,  taking  a  direc- 
tion from  the  head 
to  the  tail.  The 
movement  can  hardly 
be  seen  with  the  eye, 
although  it  is  con- 
tinued perhaps  for 
some  minutes.  The 
chr  on  ophotographic 
apparatus  should  be 
brought  to  bear  dur- 
ing such  a  period  of 
movement. 

Undulatory  Move- 
ments of  the  Skate  as 
seen  from  the  Side. — 
When  the  fish  is 
viewed  from  the  side, 
a  series  of  photo- 
graphs may  be  ob- 
tained such  as  ap- 
pears in  Fig.  154. 
The  undulatory 
movements     com- 


&  —  _ .  .^^. . - . 


Fig.  154.— Undulations  of  the  tins  of  a  skat?, 
viewed  from  the  side. 


mence  at  the  anterior  end  of  each  fin,  and  are  propagated 
in  a  posterior  direction,  increasing  in  amplitude  as  they 
proceed.  As  fresh  portions  of  the  fins  are  raised,  those 
behind  are  lowered,  so  that  the  centre  of  the  wave, 


LOCOMOTION   IN   WATER 


221 


namely,  the  most  elevated  part,  travels  rapidly  from 

the  head  towards  the  tail.     Having  rim  its  course,  the 

wave  elevates  the  posterior  extremity  of  the  fin,  and 

then  disappears.     But  another 

wave   is    already   commencing 

at   the   anterior  end,  growing 

larger,  and  travelling  along  in 

the  same  way  as  the  one  which 

preceded    it,    and    so    on    ad 

infinitum. 

It  would  be  interesting  to 
observe  what  disturbances  are 
caused  in  the  water  by  these 
undulatory  movements.  This 
could  be  ascertained,  we  think, 
by  introducing  into  the  aqua- 
rium some  of  those  little  bright 
beads  which  served  to  show  all 
the  movements  in  liquids  men- 
tioned in  Chapter  VI.  We 
by  no  means  despair  of  obtain- 
ing photographs  of  a  skate 
swimming  in  the  normal  free 
state — it  is  only  a  matter  of 
time  and  patience. 

Undulatory  Movements  of  the 
Skate  as  seen  from  the  Front. — 
With  the  express  object  of 
studying  the  movement  of  the 
fins  from  another  point  of  view, 
we  fixed  the  animal  in  a  new 
position,  by  giving  half  a  turn 
to  the  iron  framework. 

In  this  new  arrangement   the  axis  of  the  fish  ran 
in  an  antero-posterior  direction,  the  head  facing  the 
photographic   apparatus.     The   series   of  photographs 
16 


Fig.  155. — Undulations  uf  the  fins  of 
a  skate,  viewed  from  in  iront. 


222  MOVEMENT 

(Fig.  155)  shows  how  the  skate  raises  and  lowers  the 
flexible  edges  of  its  fins,  or,  rather,  how  the  resistance 
of  the  water  elevates  them  when  the  base  of  the  fin  is 
lowered.  When  we  come,  later  on,  to  demonstrate  the 
appearance  of  a  bird's  wing  as  it  strikes  the  air  the 
same  appearance  will  be  noticed.  In  fact,  the  two 
movements  have  the  same  effect,  both  propel  a  fluid 
by  an  oblique  movement  of  an  inclined  plane. 

The  undulatory  movements  of  the  skate  which  we 
have  just  described,  and  which  are  apparently  due  to 
the  co-ordinated   action  of  successive  portions  of  the 


p 

& 

Wk 

Jfk 

"■%%3- 

*^mF 

P 

f 

f 

m 

u 

Fig.  156.— Sea-horse,  showing  the  successive  and  ascending  phases  of  the  undulations 
of  the  dorsal  fin  as  the  animal  descends  through  the  water. 

fins,  is  similarly  to  be  found  in  other  aquatic  species. 
Cuttle-fish  move  their  lateral  fins  with  a  very  similar 
motion,  as  far  as  one  can  judge  by  simple  observation, 
for  we  have  not  yet  had  an  opportunity  of  photo- 
graphing the  movements  of  these  molluscs.  It  is  a 
remarkable  fact  that  cuttle-fish  can  alter  at  will  the 
direction  in  which  the  movements  of  their  fins  are 
propagated.  They  can  be  seen  swimming  in  an 
aquarium  either  to  the  right  or  to  the  left  without 
turning  round.  If  they  advance,  the  undulating  move- 
ment of  their  fin  passes  from  the  head-end  towards  the 
tail ;  if  they  go  backwards,  the  wave  passes  in  the  con- 
trarv  direction.     It  must,  however,  be  understood  that 


LOCOMOTION   IN   WATER  223 

this  alteration  in  the  direction  is  entirely  independent 
of  the  action  of  the  siphon.  Even  in  molluscs  of  too 
humble  an  organization  for  such  co-ordinated  move- 
ments progression  by  means  of  a  wave-like  movement 
may  be  observed. 

Fresh-water  tortoises  swim  in  various  ways;  generally 
their  mode  of  progression  is  something  like  that  of 
quadrupeds ;  that  is  to  say,  with  diagonally  associated 
movements  of  the  limbs,  noticeable,  for  instance,  in 
trotting. 

In  exclusively  marine  species,  the  feet  are  shaped 
something  like  fins,  or,  rather,  like  wings,  and  the 
movement  of  the  anterior  appendages  is  much  like 
that  of  a  bird.  The  result  is  a  kind  of  flight  through 
the  water,  something  similar  to  that  of  a  penguin. 
This  kind  of  locomotion,  which  we  have  as  yet  had 
no  opportunity  of  studying  by  means  of  chrono- 
photography,  is  a  functional  link  between  chelonians 
and  birds — animals  which  are  closely  allied  in  morpho- 
logical characteristics. 

Slow  Movements  of  Star-fish. — The  slow  movements 
of  certain  aquatic  animals  are  easily  studied  by  means 
of  a  series  of  photographs,  and  they  form  an  interesting 
subject  of  investigation.  Xothing  is  more  fascinating 
than  to  watch  the  evolutions  of  a  star-fish,  which  has 
turned  on  to  its  back,  in  its  attempts  to  regain  its 
normal  position.  It  finally  succeeds  by  extraordinary 
feats  of  equilibration.  It  can  be  seen  (Fig.  157) 
gradually  insinuating  one  of  its  rays  beneath  its  body, 
while  it  raises  two  others  until  its  centre  of  gravity 
is  outside  the  base  of  support.  Then,  all  of  a  sudden 
losing  its  balance,  it  falls  forwards  on  to  its  ventral 
surface.  There  is  now  nothing  left  to  be  done  except 
to  extend  its  rays  and  gradually  assume  its  normal 
position.  It  then  moves  along  the  bottom  of  the 
aquarium  with  a  crawling  motion  peculiar  to  star-fish. 


224  MOVEMENT 


Fig.  157.— Phases  of  the  movemeuta  of  a  star-fish  in  turning  itself  over.    Series  of 
images  to  be  read  from  below  upwards. 


LOCOMOTION  IN  WATER 


225 


This  somersault  takes  some  time  to  accomplish,  usually 
teu  to  twenty  minutes ;  therefore  at  least  an  interval 
of  one  minute  should  be  allowed  between  two  succes- 
sive photographs  if  the  various  phases  are  to  be  clearly 
depicted. 

Locomotion  of  Small  Marine  Animals.— If  the  move- 
ments are  small,  and  if  they  have  to  be  studied  at  a 
near  distance,  a  special  arrangement  must  be  adopted. 
Two  cover  glasses  should  be  cemented  together,  and 
a  small  aquarium  made  just  about  the  same  size  as 


Fig.  158. — Movement  of  the  appendages  of  a  shrimp. 

the  field  of  the  intended  photograph.  The  case  is 
then  filled  with  sea- water,  and  the  animal  —a  shrimp, 
for  instance  —  introduced  ;  by  taking  on  a  moving 
film  successive  photographs,  which  are  silhouetted 
against  a  luminous  background,  a  series  of  pictures 
representing  the  movements  of  the  appendages  is 
obtained. 

Further  on,  a  similar  arrangement  for  the  study  of 
the  flight  of  insects  will  be  described.  Finally,  these 
small  animals  can  be  studied  under  a  microscope  by 
an  arrangement  presently  to  be  described. 


CHAPTER  XIII 

AERIAL   LOCOMOTION 
The   Flight  of  Birds 

Summary.  — Borelli's  theory  on  the  mechanism  of  the  flight  of  birds — 
Chronography  used  for  determining  the  frequency  of  the  move- 
ments of  the  wing,  and  the  relative  duration  of  the  rise  and  fall 
— Myography— Method  of  recording  the  phases  of  contraction 
and  relaxation  of  the  wing  muscles — Record  of  the  trajectory  of 
a  bird's  humerus,  and  the  variations  in  inclination  of  the  surface 
of  the  wing— Photographic  trajectory  of  the  tip  of  the  wing — 
Chronophotography  as  showing  the  successive  attitudes  of  the 
bird  during  the  different  phases  of  movement  of  the  wings  — 
Photographs  of  birds  taken  from  different  aspects — Simultaneous 
chronophotography. 

Of  all  kinds  of  locomotion,  as  existing  among  verte- 
brates, that  of  birds  has  remained  the  longest  unex- 
plained. In  a  rather  obscure  passage,  Borelli  cornj)ares 
the  wing  action  to  that  of  a  wedge ;  meaning  by  that 
■expression  that  the  surface  of  the  wing  bears  an 
oblique  relationship  to  the  direction  of  movement, 
and  that  the  resistance  of  the  air  can  be  resolved  into 
two  separate  forces,  one  of  which  sustains  the  weight 
of  the  bird,  while  the  other  urges  it  in  a  forward 
direction.  This  interpretation  is  legitimate  in  view 
of  the  analogy  correctly  established  by  Borelli  between 
the  propelling  action  of  the  wing  and  that  of  a  fish's 
tail. 

Being   ourselves   extremely  interested   in   the  me- 
chanical problem  of  flight,  we  have  for  several  years. 


AERIAL  LOCOMOTION  227 

past  occupied  ourselves  in  determining  the  .nature  of 
the  wing  movements,  and  to  this  end  we  have  adapted 
every  possible  means  of  mechanical  appliance.  These 
experiments  furnished  us  with  important  information 
regarding  the  frequency  of  movement,  and  the  reasons 
for  variation.  We  also  obtained  records  of  the  muscular 
contractions  which  occurred  in  flight,  and  their  varia- 
tions among  different  species  of  birds.  Even  the 
trajectory  of  the  point  of  the  wing,  and  the  inclination 
of  the  wing-surface  during  the  different  phases  of 
movement,  have  been  determined  by  this  method.  It 
is,  however,  chiefly  by  means  of  chronophotography 
that  the  complicated  actions  involved  in  the  flight  of 
birds  has  been  fully  explained. 

As  we  have  fully  described  these  experiments  else- 
where,* we  need  only  refer  briefly  to  the  two  methods 
which  have  thrown  new  light  upon  this  subject. 

Employment  of  Chronophotography  in  detennining  the 
Duration  of  the  Rise  and  Fall  of  the  Wings. — As  in 
the  case  of  terrestrial  locomotion,  it  is  by  mechanical 
means  that  the  frequency  of  a  bird's  movements,  and 
the  phases  of  muscular  activity  which  result  in  flight, 
can  be  best  ascertained. 

Chronography  and  myography  have  both  been  suc- 
cessfully used  in  these  determinations.  To  measure 
the  frequency  of  the  wing  movements  an  electric 
chronograph  was  employed  to  register  on  a  revolving 
cylinder  the  make  and  break  of  an  electric  current, 
the  interruption  being  brought  about  directly  by  the 
movements  of  the  wing.  For  this  purpose  the  bird 
had  a  small  flexible  plate  fixed  to  the  extremity  of 
one  of  its  remiges,  which  was  bent  in  different  direc- 
tions by  the  resistance  of  the  air  as  the  wing  was 
raised  or  lowered.  A  double  and  very  flexible  wire 
connected  the  bird  with  the  chronograph  and  battery, 

*  Le  Vol  des  Oiseaux.     Paris,  Masson,  1890. 


228  MOVEMENT 

so  that  the  bird  could  fly  freely  about  in  a  large  room. 
The  descent  of  the  wing  closed  the  current,  and  during 
its  ascent  the  current  was  broken,  so  that  each  flap  of 
the  wing  left  a  mark  on  the  cylinder,  just  such  as 
that  caused  by  the  rise  and  fall  of  a  man's  foot  in 
walking. 

By  counting  on  the  tracing  the  number  of  ascents 
and  descents  executed  by  the  wing  in  a  given  time, 
the  frequency  of  wing  movement  proper  to  each  species 
could  be  obtained  with  the  greatest  exactness. 

It  will  be  noticed  that,  following  the  general  laws 
applicable  to  living  beings,  the  smallest  birds  have 
the  most  rapid  movements ;  the  sparrow  giving  twelve 
strokes  to  the  second,  the  pigeon  eight,  and  the 
buzzard  three.  The  relative  duration  of  the  rise  and 
fall  of  the  wing  can  be  measured  by  means  of  the  same 
chronographic  tracing.  These  two  phases  are  of  un- 
equal duration,  especially  in  the  case  of  large-winged 
birds,  the  duration  of  descent  being  considerably 
longer  than  the  period  of  ascent.  This  is  entirely 
contradictory  to  all  preconceived  notions.* 

Registration  of  Muscular  Actions. — Mechanical  regis- 
tration is  the  only  means  we  have  at  present  for 
determining  the  phases  of  contraction  and  relaxation 
of  the  wing  muscles.  A  pigeon  (Fig.  159)  is  provided 
with  a  closely  fitting  corset,  under  which  is  slipped 
a  "  myographic  capsule,"  which  is  arranged  so  as  to 

*  "  By  means  of  this  method  we  have  been  enabled  to  demonstrate 
experimentally  one  of  the  most  important  points  in  the  mechanism  of 
flight,  namely,  that  the  wing  meets  with  greater  resistance  from  the 
air  the  mure  rapid  the  progression  of  the  bird.  It  appears  that  if  a  bird 
is  travelling  at  a  certain  rate  it  continually  comes  in  contact  with  fresh 
resistance  from  the  air,  and  it  is  the  inertia  of  these  new  masses  of 
air  which  has  constantly  to  be  overcome.  On  the  other  hand,  if  the 
bird  is  stationary  when  it  takes  a  stroke  witii  its  wings,  the  air  which 
is  struck  disappears  from  under  the  wing  and  offers  no  more  resistance. 
Hence  it  is  that  if  a  bird  intends  to  take  flight,  it  first  tries  to  acquire 
a  certain  velocity,  either  by  taking  a  run,  or  by  dropping  a  certain 
distance  from  an  elevated  position."— Le  Vol  desOiseaux,  p.  249. 


AEEIAL  LOCOMOTION 


229 


record  the  contractions  of  the  pectoral  muscles.  A 
long  flexible  tube  unites  the  capsule  and  the  chamber 
of  a  recording  tambour.  This  tube  does  not  impede 
the  bird's  flight,  but  allows  a  record  to  be  obtained 
which  shows  variations  according  to  the  species  of  bird 
used  in  the  experiment.  By  means  of  a  tuning-fork 
and  chronograph,  the  duration  of  the  different  phases 
of  muscular  action  occurring 
during  the  movements  of  the 
wings  can  be  estimated 
rJ-Q  of  a  second. 

We  will  not  dwell  upon  the 
interpretation  of  these  curves, 
since  the  variations  depend 
largely  on  questions  of  com- 
parative anatomy. 

Record  of  the  Trajectory  of 
a  Bird's  Humerus. — To  fully 
understand  the  mechanism  of 
the  wing  movement,  we  set 
up  some  rather  complicated 
apparatus  so  as  to  register 
the  trajectory  of  the  humerus 
of  the  bird  with  the  variations 
in  inclination  of  the  surface 

of  the  wing  at  different  periods  of  the  movement.  In 
different  species  we  found  the  form  of  the  curves 
slightly  different,  but  they  all  took  more  or  less  the 
shape  of  an  ellipse,  the  principal  axis  of  which  was 
directed  downwards  and  forwards.  These  experiments 
were  very  difficult  to  carry  out ;  we  succeeded,  never- 
theless, in  repeating  them  a  number  of  times  with 
practically  the  same  result,  and  the  buzzard  which  we 
used  in  the  experiments  in  the  end  became  quite  tame 
and  accustomed  to  the  apparatus. 

The  trajectory  of  the  humerus  of  the  buzzard  proved 


Fig.  159. — Myographic  record  of  the 
pectoral  muscles  of  a  bird  in  flight. 


230  MOVEMENT 

that  this  bone  described  round  the  shoulder  joint  a 
cone  with  an  elliptical  base,  and  that  the  posterior  edge 
of  the  wing  was  raised  as  the  wing  was  depressed. 
This  was  due  to  the  resistance  of  the  air.  After  the 
phase  of  depression  was  over,  the  feathers,  by  reason 
of  their  resiliency,  returned  to  their  natural  position, 


Fro.  160.— Myographic  curves  taken  from  different  birds  in  Bight.  Line  I,  chrono- 
graphic  curve  100  vibrations  to  the  second.  Line  II,  tracing  of  a  pigeon's  muscle. 
Line  III,  duck's  muscle.  Line  IV,  buzzard's  muscle.  Line  V,  hawk's  muscle*. 
In  all  the  tracing  the  undulations  a  correspond  lo  the  elevation  of  the  wing  and 
the  undulations  b  to  the  descent. 

so  that  during  the  period  of  the  rise  the  under  surface 
of  the  wing  was  turned  slightly  forwards. 

Chronophotography  applied  to  the  Study  of  Flight.— 
It  might  be  urged  that  the  apparatus  which  was  fitted 
to  the  bird  could  modify  the  character  of  its  flight. 
So  no  sooner  had  we  devised  the  chronophotographic 
method  than  we  made  use  of  it  to  control  the  results 
obtained    by  purely  mechanical  means.     The  results 


AERIAL  LOCOMOTION 


231 


232  MOVEMENT 

were  not  only  fully  confirmed,  but  this  new  method 
also  completely  explained  the  movements  of  flight. 

In  this  research,  as  in  those  on  different  kinds  of 
locomotion,  it  was  necessary  to  combine  several 
methods,  each  with  its  own  particular  object.  Direct 
registration,  with  its  continuity  of  record,  was  always 
made  use  of  when  it  was  necessary  to  determine 
the  frequency  and  duration  of  a  given  movement 
of  a  part  of  the  body.  Chronophotography  was 
useful  when  a  general  idea  of  the  movement  was 
desired ;  it  was  also  the  only  means  by  which 
the  movements  of  an  isolated .  point  could  be  ex- 
pressed, when  the  movement  was  not  accompanied  by 
the  development  of  a  certain  amount  of  force.  An 
example  of  this  kind  may  be  seen  in  the  trajectory 
described  by  the  extremity  of  a  wing.  It  is  impossible 
to  apply  a  registering  apparatus  to  the  end  of 
a  flexible  feather  ;  but  the  true  interest  of  chrono- 
photography lies  in  the  fact  that  it  can  provide  a 
complete  picture  of  a  bird,  in  the  various  attitudes  it 
assumes  during  the  act  of  taking  a  stroke  with  its  wings. 

Successive  Photographs  of  Birds  taken  on  the  Wing. — 
If  a  white  bird,  brightly  illuminated  by  the  sun,  is 
photographed  in  series  as  it  crosses  in  front  of  a  dark 
background,  its  various  attitudes  will  be  clearly  seen. 
In  these  photographs  the  bending  of  the  wings  due 
to  the  resistance  of  the  air  is  usually  quite  evident, 
and  it  expresses  in  a  striking  manner  the  force  with 
which  the  wing  is  moved ;  if  one  tries  to  reproduce  the 
same  degree  of  bending  by  mere  manual  force  one  is 
quite  astonished  at  the  amount  necessary.  This  curving 
of  the  feathers  may  be  observed  in  all  kinds  of 
birds,  but  in  different  degrees  according  to  the 
flexibility  of  the  wings  ;  thus,  for  instance,  it  is  very 
pronounced  in  the  case  of  a  flying  heron,  just  when 
the  wing  reaches  the  mid  phase  of  descent  (Fig.  163). 


AERIAL  LOCOMOTION 


233 


234 


MOVEMENT 


Photographs  of  Birds  taken  from  Different  Aspects. — 
If  one  is  dealing  with  a  movement  which  is  quite 
invisible  to  the  unaided  eye,  a  single  series  of  photo- 
graphs taken  only  from  one  point  of  view  is  usually 
quite  insufficient ;  it  does  not  give  an  accurate  idea  of 
the  movement  at  any  particular  moment.  Therefore, 
it  is  desirable  to  take  photographs  from  one  or  two 
different  angles.  For  instance,  one  photograph  should 
be  taken  as  the  bird  is  flying  towards  the  camera ; 
another  as  it  flies  across  it ;  and  a  third  should  be 
taken   from   above,  with   the   camera  looking    down- 


Fig.  164.— Flight  of  a  pigeon.     The  photograph  is  taken  from  above  (cbronophoto- 
graph  on  a  fixed  plate,  25  images  to  the  second). 

wards.  Fig.  164  shows  a  photograph  of  a  pigeon 
taken  from  above.  The  camera  was  directed  vertically 
downwards  at  a  distance  of  12  metres  from  the  bird. 
In  spite  of  the  confusion  resulting  from  so  many 
images  (25  to  the  second),  the  curious  positions  of  the 
wings  at  different  moments  are  clearly  shown.  The 
various  positions  can  easily  be  distinguished  after  a 
little  practice  in  interpreting  the  meaning  of  this  kind 
of  photography. 

Chronophotography    on    Moving    Films. — To   take   a 
large  number  of  images  per  second  without  confusion, 


AERIAL   LOCOMOTION 


235 


236 


MOVEMENT 


recourse  must  be  had  to  chronophotography  on  moving 
films.  By  making  use  of  a  dark  background  we  have 
obtained  as  many  as  60  distinct  images  per  second. 
Fig.  165  is  an  example  of  this  kind ;  the  film  is  cut 
into  six  pieces,  which  are  placed  side  by  side  in  the 
illustration.  The  images  are  numbered  in  ordinary 
the  order  in    which  they  were 


figures,  according   to 
taken. 


Simultaneous   Photographs  of  the  Same   Bird   taken 


Fig.  166.— Arrangement  of  the  three  dark  backgrounds  and  the  three  cameras  for 
simultaneous  photograph y  of  a  flying  bird,  as  seen  from  three  points  of  view. 

from  Different  Aspects. — If  we  want  to  analyze  the 
movements  of  flight  with  extreme  exactness,  the  bird 
must  be  photographed  from  several  points  of  view. 
Three  cameras  are  usually  required  for  this  purpose, 
as  well  as  three  dark  screens  against  which  the  object 
is  clearly  visible.  The  arrangement  is  represented 
in  Fig.  166. 


AERIAL   LOCOMOTION 


237 


By  this  means  we  were  able  to  obtain  the  attitudes 
of  the  bird  in  three  series :  from  the  front,  from  the 


side,  and  from  above.     The  three  sets  of  photographs 
17 


238  MOVEMENT 

were  made  to  correspond  to  the  same  attitudes*  for 
convenience  of  comparison,  and  to  show  the  exact 
position  in  space  of  the  body  and  wings  (Fig.  167). 

From  these  photographs  we  have  been  able  to  con- 
struct a  series  of  bas-reliefs  showing  the  successive 
attitudes  of  the  bird. 

This  kind  of  representation  is  almost  the  only  way 
of  illustrating  the  actual  movement  during  flight,  for 
mere  ocular  observation  would  not  give  the  least  idea. 

*  '•  We  need  not  here  repeat  the  analysis  of  these  photographs,  which 
have  afforded  us  complete  information  of  the  movements  of  birds  from 
the  point  of  view  of  kinetics,  and  from  which  we  have  attempted  to 
measure  the  amount  of  work  performed  during  the  act  of  flying  by 
means  of  the  degree  of  acceleration  imparted  to  the  body." — See  Le 
Vol  ties  Oiseaux,  p.  324. 


CHAPTER   XIV 

AERIAL   LOCOMOTION 

The  Flight  of  Insects 

Summary. — Frequency  of  tlie  movements  of  insects'  wings  as  estimated 
by  the  sound  produced  in  flying — Mechanical  registration  of  the 
movements  of  the  wings ;  frequency  among  different  species — 
Synchronous  movements  of  the  wings — Changes  in  inclination 
of  the  wing  surface — Trajectory  of  an  insect's  wing — Its  inter- 
pretation—Experiments  to  demonstrate  the  direction  of  move- 
ment of  the  wins:,  and  its  variations  in  plane — The  artificia1 
insect — Theory  of  the  flght  of  insects — Photography  as  applied 
to  the  study  of  insect  flight—  Lendenfeld's  experiments — Trajec- 
tory of  the  wing  as  the  insect  advances — Photography  on  moving 
films — Arrangement  of  the  experiment— Different  types  of  flying 
insects.  Bees,  flies,  tipulae — Substantiation  of  the  mechanical 
theory  of  flight. 

Frequency  of  the  Movements  of  Insects'  Wings  as  es- 
timated by  the  Sound  produced  in  Flying. — The  flight  of 
insects  is  accompanied  by  a  humming  sound,  which  is 
of  somewhat  low  pitch  in  the  larger  species,  and  of 
very  high  pitch  in  some  of  the  smaller  insects,  such  as 
mosquitoes.  The  wings  of  insects  may  be  regarded 
simply  as  vibrating  wires,  and  hence  the  frequency  of 
their  movements  can  be  calculated  by  the  note  pro- 
duced. But  then  it  must  be  taken  for  granted  that 
the  four  wings  of  an  hymenopterous,  or  the  two  wings  of 
a  dipterous  insect  vibrate  in  perfect  unison.  In  calcu- 
lating the  frequency  of  the  movement  of  the  wings 
by  this  method,  the  following  difficulty  may  be  met 
with.      If  we  listen  to  a  fly  on  the  wing,  it  will  be 


240  MOVEMENT 

noticed  that  the  character  of  the  sound  continually 
changes.  By  close  attention,  the  sound  can  be  dis- 
tinguished as  of  a  higher  pitch  when  the  fly  approaches 
the  observer,  and  of  lower  pitch  as  it  recedes.  This 
suggests  that  there  must  be  an  alteration  in  the 
frequency  of  the  wing  vibrations.  The  phenomenon 
may,  however,  fairly  be  compared  to  the  apparent 
variations  in  shrillness  of  the  whistle  of  a  moving  train. 
As  the  train  rushes  along,  the  whistle  seems  to  become 
shriller  when  it  approaches,  and  deeper  when  it  recedes. 
This  acoustic  phenomenon  has  long  ago  been  ex- 
plained.    However,  if  we  hold  an  insect  lightly  in  a 


Fig.  168. — The  two  top  lines  are  produced  by  the  contacts  of  a  drone's  wing  on  a 
smoked  cylinder.  In  the  middle  are  recorded  the  vibrations  of  a  tuning-f  rk 
(250  vibrations  per  second)  for  comparison  with  the  frequency  of  the  wing  move- 
ments.    Below  are  seen  the  movements  of  the  wing  of  a  bee. 

pair  of  forceps  it  may  be  shown  that  when  its  wings 
vibrate  the  sound  produced  is  practically  uniform. 

Mechanical  Registration  of  the  Movements  of  Wings 
in  Insects. — The  movements  of  the  wings  of  a  captive 
insect  may  be  recorded  directly  on  a  revolving  cylinder. 
If  the  cylinder  previously  be  blackened  with  smoke 
the  slightest  touch  will  remove  the  black  and  expose 
the  white  paper  beneath.  Fig.  168  was  obtained  in  this 
way,  and  shows  several  interrupted  lines  traced  by  the 
wing  of  a  drone.  The  tracing  was  obtained  as  follows : 
The  insect  was  held  between  a  pair  of  forceps  in  such 
a  way  that  the  extremity  of  its  wing  only  just  came  in 
contact  with  the  surface  of  the  cylinder,  and  in  so 


AERIAL  LOCOMOTION  241 

doing  left  an  interrupted  track.  If  the  wing  had  been 
forced  harder  against  the  cylinder,  the  mark  left  would 
have  been  somewhat  in  the  form  of  a  comma,  and  the 
frequency  naturally  somewhat  less  owing  to  the  re- 
sistance due  to  friction.  The  same  effect  may  be 
observed  in  the  movements  of  all  kinds  of  animals. 

To  calculate  exactly  the  frequency  of  the  wing 
movements,  the  vibrations  of  a  tuning-fork  are  simul- 
taneously recorded  on  the  cylinder.  These  vibrations 
leave  on  the  blackened  paper  an  undulating  line ;  each 
vibration  representing  ^L0  of  a  second.  It  now  only 
remains  to  count  the  number  of  marks  traced  by  the 
insect's  wing  on  a  length  of  paper  corresponding  to 
250  vibrations  of  the  tuning-fork.  The  number  of 
wing  movements  per  second  is  thus  obtained. 

By  this  method  it  was  calculated  that  in  the  common 
fly  there  were  330  strokes  per  second,  in  the  bee  190, 
and  in  the  macroglossus  of  cheese  rennet  72.  Thus 
obeying  the  general  law  applicable  to  birds,  namely, 
the  smaller  the  species  the  more  rapid  the  movements 
of  the  wings. 

Synchronous  Movements  of  the  Wing's,  Variations  in 
Surface  Inclination. — There  are  other  facts  to  be  learnt 
from  direct  registration  of  the  wing  movements.  Thus 
by  holding  a  fly  in  such  a  position  that  its  two  wings 
strike  the  cylinder  at  the  same  time,  it  will  be  seen 
that  both  wings  impart  the  same  number  of  strokes, 
and  that  the  movements  are  absolutely  synchronous. 

In  some  species  of  insects  the  upper  surface  of  the 
wings  is  covered  with  fluffy  hairs,  while  the  lower 
surface  is  bare ;  tracings  taken  from  the  wings  of  such 
insects  show  alternate  variations.  Fig.  169  was 
obtained  from  Macroglossus  of  cheese  rennet,  a  small 
diurnal  hawk  moth  which  flies  very  rapidly  and  is  very 
common  in  France.  The  insect  was  held  in  such  a  way 
that  the  under  side  of  its  wing  touched  the  cylinder. 


242  MOVEMENT 

Now,  in  moving  to  and  fro,  the  wing  struck  the  cylinder 
alternately  with  the  hairy  and  smooth  surface,  which 
proved  that  the  wing  underwent  a  change  in  inclina- 
tion. This  fact  is  important  to  bear  in  mind,  for  it 
materially  elucidates  the  mechanism  of  flight.  Such 
is  the  information  derived  from  recording  insect  move- 
ment by  means  of  mechanical  methods. 

The  attempt  might  be  made  to  obtain  the  trajectory 
of  the  extremity  of  the  wing  by  a  similar  means. 

But  the  wing,  moving  as  it  does  in  all  sorts  of 
directions  round  its  thoracic  articulation,  describes  a 
spherical  figure,  the  whole  of  which  could  not  possibly 


Fig.  169. — Movements  of  the  wing  of  Macroglossus  of  cheese  rennet  on  the  surface 
of  a  smoked  cylinder. 

be  traced  on  anything  else  than  the  inner  surface  of  a 
sphere.  The  contact  of  the  wing  with  the  surface  of 
the  cylinder  could  only  take  place  to  a  very  small 
extent.  Consequently  another  method  must  be  em- 
ployed for  obtaining  the  trajectory  described  in  the 
air  by  the  extremity  of  the  wing. 

Trajectory  of  the  Extremity  of  the  Wing  —  Remember- 
ing the  fiery  tracks  left  upon  the  retina  when  a 
luminous  object  was  waved  in  front  of  the  eyes,  we 
fastened  a  spangle  of  gold-leaf  to  the  extremity  of  a 
wasp's  wing.  The  insect  was  then  seized  with  a  pair 
of  forceps  and  held  in  the  sun  in  front  of  a  dark  back- 
ground.    We  then  watched  the   luminous   trajectory 


AERIAL   LOCOMOTION 


243 


which  shaped  itself  in  the  form  of  a  lemniscate,  Fig.  170. 
The  figure  8  would  exactly  express  what  we  saw,  and 
the  resemblance  was  the  more  complete  because,  in  the 
trajectory  thus   described,   one   of  the   limbs   seemed 


Fig.  170. — Appearance  of  a  wasp  flying  in  the  sun.    The  extremity  of  the  wing  is 

gilded. 

larger  and  brighter  than  the  other.  In  describing  this 
appearance  we  ignored,  or  omitted  to  mention  the  fact, 
that  Mr.  Pettigrew,  in  England,  had  noticed  the  same 
appearance  in  a  flying  insect,  which  gave  rise  on  his 
part  to  claims  of  priority  of  discovery.  Nevertheless, 
we  may  remark  that  the  method  of  formation  of  the 
figure  described  by 
the  wing  of  an  insect, 
according  to  Mr. 
Pettigrew,    is    quite 

different       IrOni      OUr  FlG<   m._The  trajectory  of  the  anterior  and  po*- 

prmppntinn  A  ppnrrl-  terior  border  of  the  wiDS  of  an  insect  during  halt 
Conception.     .VCCOm-      an  oscillation  (Pettigrew> 

ing  to   the  English 

authority,  the  anterior  border  of  the  wing  describes  one 
limb  of  the  lemniscate  while  the  inferior  border  de- 
scribes the  other.  In  Fig.  171,  which  is  borrowed  from 
his  work,  the  arrows  indicate  a  complete  reversal  of  the 
wing  surface  in  a  simple  movement  from  left  to  right. 


244  MOVEMENT 

According  to  our  view,  on  the  contrary,  the  extremity 
of  the  wing  describes  each  limb  of  the  lemniscate  in 
succession,  in  a  dual  motion  from  left  to  right,  and 
then  from  right  to  left.  Meanwhile  the  surface  of  the 
wing  is  variously  distorted  by  the  resistance  of  the 
air.  In  Fig.  172  dotted  lines  indicate  the  direction 
of  this  distortion  which  could  never  amount  to  a  com- 
plete reversal.  Now, 
the  mechanical  theory 
which  can  be  deduced 
.rom  this  optical  figure 
depends  entirely  on  the 
manner  in  which  the 
wing    is    supposed    to 

Fig.  172.— Trajectory  of  the  anterior  order  of  ,         "    ,  «i      T  • 

tbe    wing    during    a     complete    oscillation  liave  deSCl'lbed  it.       Ac- 
(Marey).      The  small  lines  which   are   set  -. .  -..-        ^        . 

obliquely  in  various  directions  represent  the  COrCling     tO     IVll*.     X  ettl- 

inclinations  of  the  surface  of  the  wing.  ,      ,  i  .-, 

grew  s  theory,  the  revo- 
lution of  the  wing  is  active  and  due  to  the  contraction 
of  muscles.  According  to  our  theory,  the  change  in 
inclination  of  the  wing  is  passive  and  brought  about  by 
the  resistance  of  the  air,  for  it  is  only  the  posterior 
part  of  the  wing  that  is  distorted,  the  anterior  part 
being  kept  straight  and  stiff  by  a  rigid  nervure.  The 
importance  of  a  correct  interpretation  of  the  figure 
described  by  an  insect's  wing  is  very  great,  because  the 
explanation  of  the  mechanism  of  flight  depends  upon 
it.  We  have,  however,  no  desire  to  weigh  the  respective 
merits  of  the  two  theories,  we  only  wish  to  enumerate 
the  experiments  by  which  we  have  demonstrated  our 
own  views. 

Experiments  for  determining  the  Direction  taken  by 
the  Wing  in  course  of  Movement,  and  Explanation  of  the 
Mechanism  by  which  the  Alteration  in  Inclination  is 
effected. — The  optical  method,  namely,  that  of  deter- 
mining the  movements  of  the  wing  by  the  impression 
left  on  our  organs  of  sight  by  the  gold  spangle  fastened 


AERIAL  LOCOMOTION  245 

on  the  extremity  of  the  wing,  shows  that  tne  surface 
of  the  wing  is  differently  inclined  during  the  various 
phases  of  movement.  Now,  we  have  seen  that  the  two 
limbs  of  the  8  described  in  this  way  are  unequally 
luminous,  and  from  this  we  concluded  that  while  one 
of  the  limbs  was  being  described,  the  inclination  of 
wing  must  have  been  more  favourable  for  the  reflection 
of  the  sun  by  the  gold  spangle,  and  that,  while  the 
other  limb  was  being  described,  the  gold  spangle  must 
have  had  a  less  favourable  inclination.  If  this  is  so,  by 
altering  the  position  of  the  insect,  a  change  should  be 
effected  in  the  degree  of  reflection,  and  as  a  matter 
of  fact  this  is  exactly  what  does  happen.     When  the 


Fig.  173. — Experiment  to  test  the  direction  of  movement  of  an  iDsect's  wing. 

insect  is  turned  through  an  angle  of  about  90°,  what 
was  before  the  bright  limb  of  the  8  is  now  no  longer 
conspicuous,  whereas  the  other  side,  in  its  turn,  becomes 
brilliantly  illuminated.  In  this  way  the  variations  in 
inclination  can  be  demonstrated.  Even  the  angle 
formed  by  the  wing  with  the  axis  of  progression  could 
be  deduced  from  these  experiments,  but  we  shall  see 
that,  by  the  employment  of  photography,  this  angle 
varies  from  moment  to  moment.  The  most  that  one 
can  say  is  that  the  angle  is  about  45°,  sometimes  in  one 
direction,  sometimes  in  the  other. 

To  determine  with  accuracy  the  direction  taken  by 


246  MOVEMENT 

the  wing  at  different  stages  of  the  trajectory,  we  pro- 
ceeded as  follows.  A  small  piece  of  capillary  glass 
tubing  was  blackened  in  the  smoke  of  a  candle,  so  that 
the  slightest  touch  on  the  glass  was  sufficient  to  remove 
the  black  coating  and  show  the  direction  of  movement 
in  each  limb  of  the  lemniscate.  This  experiment  was 
arranged  as  shown  in  the  figure  (173).  Different 
points  on  the  path  of  movement  were  tested  by  the 
smoked  rod,  and  from  the  track  along  which  the  black 
had  been  removed  the  direction  of  movement  was 
deduced.  This  direction  is  represented  in  the  figure 
by  means  of  arrows. 

For  the  sake  of  comparison,  we  constructed  an 
artificial  insect,  the  wing  of  which  consisted,  as  in 
nature,  of  a  rigid  nervure  anteriorly,  and  a  sort  of 
flexible  sail  behind.  We  have  watched  this  little 
contrivance  move  like  a  real  insect,  give  like  it  a 
luminous  trajectory  shaped  like  a  lemniscate,  agitate 
the  air  behind,  and  by  a  kind  of  suction  action  aspirate 
air  towards  it  in  front.* 

Theory  of  Insect  Flight. — The  theory  of  insect  flight 
may  be  completely  explained  from  the  preceding 
experiments.  The  wing,  in  its  to-and-fro  movements, 
is  bent  in  various  directions  by  the  resistance  of  the 
air.  Its  action  is  always  that  of  an  inclined  plane, 
striking  against  a  fluid,  and  utilizing  that  part  of  the 
resistance  which  is  favourable  to  its  onward  progression. 

This  mechanism  is  the  same  as  that  of  a  waterman's 
scull,|  which,  as  it  moves  backwards  and  forwards,  is 
obliquely  inclined  in  opposite  directions,  each  time 
communicating  an  impulse  to  the  boat. 

There  is,  however,  a  difference   between  these  two 

*  La  Machine  Animale,  book  iii.,  chap.  ii. 

t  This  refers  to  what  is  generally  called  "sea-sculling,"  and  of 
course  has  no  reference  to  the  ordinary  river  sculling,  which  requires 
the  use  of  two  sculls. — Translator. 


AERIAL   LOCOMOTION  247 

methods  of  propulsion.  The  scull  used  by  the  water- 
man offers  a  rigid  surface  to  the  water,  and  the  operator 
has  to  impart  alternate  rotary  movements  to  the  scull 
by  his  hand — at  the  same  time  taking  care  that  the 
scull  strikes  the  water  at  a  favourable  slant.  The 
mechanism  in  the  case  of  the  insect's  wing  is  far 
simpler,  the  flexible  membrane  which  constitutes  the 
anterior  part  of  the  wing  presents  a  rigid  border, 
which  enables  the  wing  to  incline  itself  at  the  most 
favourable  angle. 

The  muscles  only  maintain  the  to-and-fro  movement, 
the  resistance  of  the  air  does  the  rest,  namely,  effects 
those  changes  in  surface  obliquity  which  determine 
the  formation  of  an  8-shaped  trajectory  by  the  ex- 
tremity of  the  wing. 

Photography  as  applied  to  the  Study  of  Insect 
Flight. — The  reader  may,  perhaps,  be  surprised  that 
we  have  not,  as  yet,  resorted  to  photography  as  a 
means  of  determining  the  trajectory  of  an  insect's 
wing,  since  this  is  the  only  method  of  recording  an 
accurate  tracing.  This  is  because  the  experiments 
just  mentioned  were  carried  out  long  before  photo- 
graphy could  be  employed  to  study  any  kind  of  move- 
ment. Photography  was  applied  by  Lendenfeld  *  for 
determining  the  position  of  the  wings  of  a  dragon-fly. 

This  author  also  showed  how  the  lemniscate  descrioed 
by  the  extremity  of  the  wing  became  displaced  and 
distorted  by  the  animal's  forward  progression.  The 
experiments  of  the  German  naturalist  were  made  on  a 
dragon-fly,  which  was  fixed  at  the  end  of  a  sort  of 
balanced  beam  ;  and  although  the  animal  could  raise 
itself  to  a  slight  degree,  the  conditions  were  not  such 
as  to  indicate  the  normal  trajectory  of  the  wing,  when 
the  in>ect  was  free  to  fly  where  it  liked. 

*  Lendenfeld,  Der  Fluq  der  Libellen,  Acad,  der  Wissenschaften. 
Vienna,  1881,  Hei't.  i.  p.  289. 


248 


MOVEMENT 


We  succeeded  in  obtaining  a  photograph  of  the 
gilded  wing  of  an  insect,  which,  though  not  absolutely 
at  liberty,  could  fly  at  a  comparatively  high  rate  of  speed. 

Photography  of  the  Trajectory  of  the  Wing. — The 
following  is  the  arrangement  we  adopted  for  our  experi- 
ments.     A  wooden   box   one   metre  square   and  025 


Fig.  174. — Insect  flying  round  and  round  in  front  of  a  dark  background. 


metre  deep,  was  lined  throughout  with  black  velvet. 
At  the  bottom  of  the  box  a  central  disc,  supported  by 
a  footpiece,  was  placed  in  position :  the  periphery  of 
the  space  was  covered  with  a  white  material,  leaving 
between  it  and  the  central  disc  an  annular  track  covered 
with  black  velvet  (Fig.  174).    It  was  round  this  annular 


AEKIAL   LOCOMOTION  249 

track  that  the  insect  was  made  to  fly.  A  needle  stuck 
perpendicularly  in  the  middle  of  the  disc  served  as  an 
axis  for  a  revolving  beam  and  its  counterbalance.  This 
beam  consisted  of  a  straw,  and  at  the  end  of  it  was 
fixed  a  light  pair  of  surgical  forceps  to  hold  the  insect 
by  a  part  of  its  abdomen.  When  thus  fastened,  the 
dragon-fly  was  left  to  its  own  devices.  It  then  com- 
menced flying  at  rather  a  rapid  rate  round  the  track, 
drawing  the  straw  after  it,  the  movement  often  per- 
sisting for  some  considerable  time.     The  gold  spangle 


Fig.  175.-  Photographic  trajectory  of  ihe  wing  of  a  dragon-fly. 


fastened  to  its  wing  described  a  trajectory  which  is 
reproduced  in  Fig.  175. 

The  lemniscate  described  by  the  insect  during  its 
flight  in  captivity,  is  no  longer  to  be  seen,  but  in  its 
place  there  is  an  undulating  curve  which  presents  at 
different  stages  of  its  course  a  greater  or  less  degree 
of  brightness,  according  as  the  inclination  of  the  wing 
is  favourable  for  the  reflection  of  light  or  the  reverse. 

Chronophotography  of  Insects  on  Moving  Films. — The 
series  of  proofs  which  we  have  just  given  appear  to 
us  to  leave  no  doubt  as  to  the  correctness  of  our  views 
on  the  flight  of  insects. 


250 


MOVEMENT 


But  although  our  theory  may  be  generally  true, 
there  are  still  certain  details  which  remain  to  be 
elucidated.  For  instance,  in  what  way  does  the  flight 
of  one  insect  differ  from  that  of  another,  and  what 
function  do  the  balancers  subserve?  Those  singular 
organs  which  from  the  point  of  view  of  comparative 
anatomy  would  seem  to  be  undeveloped  wings,  appear 
to  be  indispensable  for  the  flight  of  dipterous  insects. 
It  occurred  to  us  that  these  and  many  problems 
could  be  solved  by  chronophotography,  if  it  only 
enabled  us  to  catch  a  momentary  view  of  the  insect's 


Fig,  176.--  Schematic  arrangement  for  illuminating  insects  when  studying  their  flight. 

wing  during  its  flight.  But  one  can  imagine  that 
the  exposure  would  have  to  be  very  short  to  procure 
a  well-defined  photograph  of  an  insect's  wing,  when 
an  exposure  of  ^q-qd  °f  a  second  is  too  long  in  the 
case  of  a  bird's,  although  in  the  latter  instance  the 
movement  is  much  less  rapid. 

Further,  it  is  not  improbable  that  with  such  a  short 
exposure,  the  time  would  be  insufficient  to  imprint  a 
definite  image  on  the  plate.  In  order,  then,  to  diminish 
the  period  of  exposure  the  fenestrations  of  the  rotary 
diaphragms  must  be  made  very  small,  and  the  light 


AEE1AL   LOCOMOTION 


251 


that  is  thrown  on  the  insect  very  concentrated.  Fig. 
176  is  a  general  scheme  of  the  arrangement  we 
adopted.  In  the  first  place,  it  will  be  noticed  that 
there  is  a  parallel  beam  of*  light  travelling  from  right 
to  left,  and  directed  by  a  heliostat  towards  the  principal 
optical  axis  of  the  object-glass.  This  beam  of  light  is 
condensed   by   a   lens*  (c)  behind   which   the   insect 


Fig.  177.— Chronophotographic  apparatus  arranj 

insects. 


for  studying  the  natural  flight  oi 


can  be  seen  between  the  points  of  a  forceps.  The 
condensed  beam  of  light  traverses  the  first  lens  of  the 
object-glass,  and  the  rays  are  brought  to  a  focus  at 
the  circular  diaphragms  ;  at  the  moment  two  fenestra- 
tions coincide  the  rays  can  pass  through  and  illuminate 
the  field  of  the  movable  film,  in  the  middle  of  which 
a  silhouetted  image  of  the  insect  stands  out  in  bold 

*  The  focal  length  of  this  lens  should  be  at  least  double  that  of 
the  objective. 


252 


MOVEMENT 


contrast.  We  were  not  very  successful  in  our  experi- 
ments with  all  kinds  of  insects  ;  the  method,  it  is 
true,  allows  of  the  insect  being  posed  at  will,  and  also 
allows  one  to  obtain  photographs  of  the  attitudes  of 
the  wings  as  seen  from  different  points  of  view,  but 
it  gives  them  an  exaggerated  appearance  both  as 
regards  the  extent  and  the  rapidity  of  the  movement. 

To  study  an  insect  in  free  flight,  a  cardboard  box 
(Fig.  177)  is  placed  in  front  of  the  object-glass,  the 
insect  is  confined  by  means  of  a  pane  of  glass  which 
just  touches  the  condensing  lens.  Being  introduced 
into  this  box,  the  insect  immediately  flies  against  the 


Fig.  178. — Fly  crawling  on  a  window-pane  before  taking  to  flight. 

glass,  which  previously  should  be  placed  at  the  focal 
point  of  the  object-glass.  The  insect's  flight  can  be 
wratched,  and  at  the  desired  moment  the  button  can 
be  pressed  which  sets  the  film  in  motion. 

Fig.  178  was  obtained  in  this  way ;  it  represents  a 
fly  crawling  on  the  pane  of  glass  and  then  taking 
flight.  The  exposures  were  extremely  short,  as  we 
have  previously  mentioned,  in  order  that  the  wings, 
which  moved  very  rapidly,  might  be  well  defined. 

With  fenestrations  2  centimetres  in  breadth,  the 
actual  exposure  being  2  oV  o  °f  a  second,  the  photographs 
were  not  distinct,  at    least  not  of  the  extremities  of 


AERIAL   LOCOMOTION 


253 


the  wings.  So  we  gradu- 
ally reduced  the  diameter 
of  the  fenestrations  by 
drawing  the  metal  cur- 
tains which  regulated  the 
size  of  the  openings. 

When  the  openings  in 
the  two  diaphragms  were 
only  I'D  millimetre  in 
breadth,  the  duration  of 
the  exposure  was  reduced 
to  25  000  °f  a  second,  and 
in  this  case  the  photo- 
graphs obtained  never 
failed  to  be  absolutely 
distinct. 

An  insect  flying  against 
the  pane  of  glass  must 
occupy  a  considerable 
amount  of  space  in  an 
antero  -  posterior  direc- 
tion, and  hence  if  all 
portions  of  the  body  are 
to  be  well  defined,  the 
object-glass  must  be  one 
of  considerable  focal 
length.  Xow,  as  a  mat- 
ter of  fact,  the  extreme 
narrowness  of  the  fenes- 
tration through  which 
the  light  passes,  and  the 
corresponding  smallness 
of  the  openings  of  the 
diaphragms  give  a  focal 
length  of  rather  more 
than  2  centimetres. 
18 


254  MOVEMENT 

Fig.  179  shows  a  bee  in  various  phases  of  flight.  The 
insect  sometimes  assumes  almost  a  horizontal  position, 
in  which  case  the  lower  part  of  its  body  is  much  nearer 
the  object-glass  than  is  its  head,  and  yet  both  ex- 
tremities are  equally  well  defined  in  the  photograph. 

The  successive  images  are  separated  by  an  interval 
of  ^0  of  a  second  (a  long  time  when  compared  to  the 
total  time  occupied  by  a  complete  wing  movement,  i.e. 
j^q  of  a  second).  And  hence  it  is  useless  to  attempt 
to  gain  a  knowledge  of  the  successive  phases  of  move- 
ment, by  examining  the  successive  photographs  of  a 
consecutive  series  representing  an  insect  in  flight. 
Nevertheless,  an  examination  of  isolated  images  affords 
information  of  extreme  interest  with  regard  to  the 
mechanism  of  flight. 

We  have  seen  that  owing  to  the  resistance  of  the 
air  the  expanse  of  wing  is  distorted  in  various  direc- 
tions by  atmospheric  resistance.  Now,  as  the  oscilla- 
tions during  flight  are  executed  in  a  horizontal  plane 
the  obliquity  of  the  wing  surface  ought  to  diminish 
the  apparent  breadth  of  the  wing.  This  appearance 
can  be  seen  in  Fig.  180.  There  is  here  a  comparison 
between  two  tipulse :  the  one  in  the  act  of  flight,  the 
other  perfectly  motionless  and  resting  against  the 
glass  window. 

The  motionless  insect  maintains  its  wings  in  a 
position  of  vertical  extension,  the  plane  is  therefore 
at  right  angles  to  the  axis  of  the  object-glass.  The 
breadth  of  the  wing  can  be  seen  in  its  entirety  ;  the 
nervures  can  be  counted,  and  the  rounding  off  of 
the  extremities  of  the  wings  is  perfectly  obvious.  On 
the  other  hand,  the  flying  insect  moves  its  wings  in 
a  horizontal  direction,  and  owing  to  the  resistance  of 
the  air  the  expanse  of  the  wings  is  obliquely  disposed, 
and  only  the  projection  of  its  surface  can  be  seen 
in  the  photograph.     This  is  why  the  extremity  of  the 


AERIAL   LOCOMOTION 


255 


wing  appears  as  if  it  were  pointed,  while  the  other 
parts  look  much  narrower  than  normal.  The  extent  of 
the   obliquity   can   be    measured    from   the   apparent 


-.2 


L^. 


7m&z 


s* 


p.  ~  — ■ 

£  m  o 

"as 


alteration  in  width,  for  the  projection  of  this  plane  with 
the  vertical  is  the  sine  of  the  angle.     From  this  it 


256 


MOVEMENT 


- 

I   \lr 

*■'     "^     \ 

■•"':.''  ": 

Oil  ->^ < 

^- ' 

^fe 

f  1 

/ 

••     /7" 

■>w>/_ 

.   '    f'  f         ^~-- 

•    \ 

w 

\ 

.         /J^! 

*£': 

■^     ^i^P 

* j 

may  be  gathered 
that  the  right 
wing  (Fig.  180,  3rd 
image)  was  inclined 
at  an  angle  of  about 
50°  with  the  verti- 
cal, say  40°  with 
the  horizontal. 

This  inclination 
necessarily  varies  at 
different  points  of 
the  trajectory,  and 
must  augment  with 
the  rapidity  of 
movement ;  the  ob- 
liquity reaching  its 
maximum  in  those 
portions  of  the  wing 
which  move  with 
the  greatest  velo- 
city, namely,  to- 
wards the  extremi- 
ties. The  result  is 
that  the  wing  be- 
comes twisted  at 
certain  periods  of 
the  movement. 

The  tortion  which 
was  reproduced  in 
the  case  of  the  wings 
of  our  artificial  in- 
sects, may  be  ob- 
served in  some  of  the 
photographs,  as,  for 
instance,  in  the  4th 
image  in  Fig.  181. 


AEKIAL   LOCOMOTION  257 

AY  hen  the  direction  of  movement  varies,  the  inclina- 
tion of  the  plane  of  the  wing-  varies  also,  and  for  a 
moment  this  plane  must  become  vertically  disposed. 
This  may  be  seen  in  the  first  image  of  the  same  figure, 
for  in  this  instance  the  wing  looks  exactly  the  same 
size,  and  has  the  same  appearance,  as  in  the  case  of 
the  motionless  insect. 

The  balancers  can  be  distinctly  seen,  and  the  posi- 
tion of  these  organs  seems  to  vary  according  to  that  of 
the  wings.  Careful  observation  of  a  great  number  of 
photographs  taken  under  different  conditions  will  no 
doubt  determine  the  nature  of  the  movements  of  these 
structures. 

Finally,  we  by  no  means  despair  of  being  able  to 
apply  chronophotography  on  fixed  plates  to  the  study 
of  insect  movement,  and  of  thus  being  able  to  obtain 
a  sufficient  number  of  photographs  to  demonstrate  all 
the  phases  of  the  wing  movement. 

Some  of  our  attempts  have  already  shown  that  under 
certain  conditions  of  illumination,  the  insect  can  be 
photographed  as  a  bright  object  standing  out  against 
a  dark  background. 


CHAPTER  XV 

COMPARATIVE   LOCOMOTION 

Summary.— Comparative  locomotion  among  terrestrial  mammals:  the 
man,  the  horse,  the  elephant — Comparative  locomotion  among 
different  kinds  of  birds — Classification  of  different  types  of  loco- 
motion— Comparative  locomotion  of  tortoises  and  lizards  ;  frogs, 
toads,  and  tadpoles  ;  snakes,  eels,  and  fish  ;  insects  and  spiders. 

Comparative  Locomotion.  —  The  most  interesting 
feature  of  zoology  is  not  so  much  the  descriptive  and 
systematic  account  of  the  various  forms  met  with  in  the 
animal  kingdom  as  the  tracing  of  association  between 
form  and  function.  As  comparative  anatomy  and 
physiology  become  more  and  more  allied,  doubtless 
more  fundamental  morphological  laws  will  be  dis- 
covered, and  these  perhaps  will  enable  us  to  predict 
the  function  of  any  particular  organ  from  an  ana- 
tomical inspection. 

We  are  certainly  very  far  from  being  in  a  position 
to  understand  this  association  in  the  case  of  most 
organs ;  but  the  mechanical  action  of  some  of  them 
is  already  so  familiar  that  the  physiological  function 
can  be  explained  on  anatomical  grounds.  The  form 
of  the  vertebrate  skeleton,  the  volume  and  length  of 
the  muscles,  and  the  relative  dimensions  of  the  long 
bones  are  necessarily  closely  associated  with  the  kind 
of  locomotion  habitual  to  the  animal.  Inviolable 
mechanical  laws  govern  this  association,  some  of  them 


COMPARATIVE   LOCOMOTION  259 

have  already  been  enunciated,  and  we  have  no  doubt 
that  others  will  soon  receive  an  accurate  formulation. 

But  to  determine  these  laws  the  character  of  an 
animal's  locomotion  must  be  as  precisely  defined  as 
its  anatomical  structure.  Chronophotography,  and 
more  particularly  the  diagrams  which  it  enables  us  to 
construct,  leave  nothing  to  be  desired  in  point  of 
truthful  expression  of  certain  types  of  locomotion.  A 
few  examples  will  show  the  value  of  this  method. 

Comparative  Locomotion  among  Different  Terrestrial 
Mammals. — A  striking  feature  among  terrestrial  mam- 
mals is  the  variety  of  morphological  form,  and  this  is 
equally  the  case  as  regards  their  mode  of  locomotion. 
But  beneath  this  apparent  diversity,  zoologists  have 
discovered  profound  analogies;  only  to  instance  the 
most  obvious  of  these,  the  lower  limbs  of  a  man 
evidently  correspond  to  the  hind  legs  of  a  quadruped, 
and  all  through  the  mammalian  series  some  similarity 
may  be  recognized,  either  as  regards  limb  or  bone  or 
muscle.  Differences,  indeed,  exist  among  different 
species,  but  they  are  chiefly  referable  to  inequality  of 
development,  fusion  of  some  parts,  atrophy  or  mal- 
formation of  others,  or  to  anatomical  disproportion.  The 
important  point  to  establish  is  the  connection  between 
anatomical  and  functional  variation. 

Xow,  by  means  of  chronophotography,  it  is  easy  to 
trace  among  different  species  the  respective  movements 
of  the  different  segments  of  the  limb  in  walking  or 
running.  One  animal  supports  itself  on  the  ground 
by  its  digital  extremities,  another  by  the  entire  plantar 
surfaces  of  the  feet.  One  animal  will  progress  by 
means  of  alternate  oscillations  of  its  limbs,  another  by 
sudden  extension  ending  in  a  jump.  But  the  unaided 
eye  cannot  determine  with  certainty  the  respective 
parts  played  in  these  actions  by  the  various  bony 
segments.     Chronophotography,  however,  shows  every 


260 


MOVEMENT 


detail  with  absolute  accuracy.  Thus  the  diagrams 
182,  183,  and  184  represent  almost  on  the  same  scale 
the  movements  of  the  different  segments  of  the  lower 


Fig.  182. — Movement?  of  a  uiai 


in  executing  a  step. 


limbs  during  the  execution  of  half  a  step  in  the  case 
of  a  man,  a  horse,  and  an  elephant. 

These  diagrams  demonstrate  that  the  same  segment 
can  execute  different  movements,  just  as  it  may  be  of 
different  length  and  different  shape  in  the  three  types 
under  comparison,   and  that  the  same  segment   may 


Fig.  183. — Movements  of  the  various  segments  of  a  horse's  hind  leg  in  executing  a 

step. 

play  a  variable  part  in  the  flexion  and  extension  of  the 
limb. 

We  can  now  understand  why  the  muscles  which  act 
upon  these  bones  present,  in  different  species  of 
animals,  differences  in  length  and  volume,  although  the 


COMPARATIVE   LOCOMOTION 


2(51 


movement  executed  may  be  the  same.  It  is  by  thus 
analyzing  the  types  of  locomotion  proper  to  a  large 
number  of  species  that  the  necessary  data  is  forth- 
coming for  determining  the  association  between  form 
and  function.* 

In  returning  to  the  study  of  man,  the  significance 
of  individual  peculiarities  in  the  structure  of  the 
body  will  make  itself  apparent.  The  variation  in 
length  of  the  bones  of  the  limbs,  or  in  the  develop- 
ment of  certain  muscles,  so  noticeable  among  certain 
races  of  men,  connects  each  human  type  with  some 


Fig.  184. — Movements  of  an  elephant's  bind  leg  in  executing  a  step. 

species  of  animal  with  similar  characteristics.  If,  for 
instance,  the  development  of  the  gastrocnemius  muscle, 
or  extensors  of  the  thigh,  in  a  man  suggests  a  resem- 
blance to  a  leaping  animal,  it  may  be  concluded  that 
this  man  will  probably  possess  special  aptitude  for 
jumping,  and  so  on. 

Comparative  Locomotion  among  Birds. — We  know 
that  there  are  two  distinct  types  of  wing  among 
birds,  each  suitable  for  a  different  kind  of  flight,  the 
"  sailing  "  flight  and  the  "  rowing  "  flight.  Birds  that 
sail  possess  narrow  wings ;  shorter  and  broader  wings 
are  peculiar  to  those  that  use  them  as  oars.     If  the 

*  See  Marey,  Recherches  Experiment  ales  sur  la  Morphologie  des 
Muscles.     C.  K.  de  l'Academie  des  Sciences,  September  12,  1887. 


262  MOVEMENT 

area  of  wing  is  greatly  reduced,  the  bird  can  fly  no 
longer  in  the  ordinary  way  through  the  air;  but  it 
can  fly  fairly  well  along  the  water,  like  penguins  and 
birds  of  similar  nature.  This  water-flight  may  be 
observed  also  among  certain  marine  tortoises,  the  lower 
limbs  of  which  resemble  in  shape  the  wings  of  a 
penguin.  Further,  tortoises  and  birds  have  many 
anatomical  resemblances. 

The  relation  between  the  shape  of  the  wing  and 
the  character  of  flight  can  be  traced  as  regards  other 
structural  details.  We  have  already  shown  that  the 
volume  and  shape  of  the  muscles  present  differences 
amongst  birds  which  use  their  wings  as  sails  and  those 
which  use  them  as  oars ;  in  the  former  the  muscles 
are  short  and  thick,  in  the  latter  long  and  slender. 
Similar  differences  are  to  be  noticed  in  the  bones  of 
the  thorax  which  are  characteristically  grooved  for  the 
insertion  of  these  muscles. 

The  differences  in  flight  among  the  principal  types  of 
birds,  as  far  as  we  have  been  able  to  study  them,  have 
been  demonstrated  by  means  of  chronophotography, 
and  it  is  extremely  probable  that,  by  studying  a  great 
number  of  species  by  the  same  method,  we  shall  find 
among  the  various  types  of  flight,  gradations  and 
transitions  parallel  to  those  anatomical  variations 
which  have  been  recognized  by  comparative  anatomists 
among  ornithological  genera  and  species. 

Classification  of  Different  Types  of  Locomotion. — It  is 
not  always  possible  to  take  comparative  anatomy  as 
a  guide  to  physiological  classification.  Sometimes  it 
is  the  variation  or  functional  analogy  which  may  be 
most  apparent,  and  which  will  assist  us  in  discovering 
the  zoological  relationship.  For  this  reason  we  have 
endeavoured  to  procure  photographs  of  a  great  number 
of  different  species  of  animals,  so  as  to  collate  the 
various  physiological  types  and  classify  them  like  the 


COMPAKATIVE  LOCOMOTION  263 

sections  of  a  museum  of  comparative  anatomy,  in 
the  hope  that  such  a  series  might  be  able  to  throw 
some  light  upon  the  subject.  The  principal  difficulty 
in  this  undertaking  lies  not  so  much  in  the  actual 
collection  of  many  different  species,  as  in  the  sub- 
jection of  them  to  the  best  conditions  for  observation. 

Domestic  animals  or  tame  species  can  easily  be  dealt 
with,  but  the  natural  paces  or  movements  of  others 
can  only  be  observed  under  special  conditions,  the 
nature  of  which  can  only  be  discovered  after  patient 
research. 

A  frightened  animal  never  moves  about  in  a  normal 
fashion,  and  if  it  is  compelled  to  advance  in  a  pre- 
determined direction,  it  instinctively  goes  the  other  way. 
Sometimes  the  animal  becomes  scared  by  the  bright 
light  with  which  it  is  necessarily  illuminated ;  at  other 
times  it  resents  an  abnormal  support  under  its  feet. 
In  some  cases  the  animal  has  to  be  brightly  illu- 
minated against  a  dark  background,  at  others  it  has 
to  be  silhouetted  against  a  dark  background.  In  all 
these  cases  a  straight  pathway  from  which  it  cannot 
diverge  is  essential. 

Being  compelled  to  curtail  the  discussion  of  these 
researches,  we  can  only  give  a  few  examples  of 
comparative  locomotion,  and  a  brief  account  of  the 
arrangements  for  taking  the  photographs. 

Comparative  Locomotion  of  Tortoises  and  Lizards.  —A 
water  tortoise  was  placed  in  a  glass  aquarium  and 
exposed  to  translucent  illumination,  just  as  in  the  case 
of  the  sea-horse  described  (p.  212).  The  animal  dived 
and  crawled  about  at  the  bottom  of  the  aquarium,  but 
after  a  time  it  had  to  rise  to  the  surface  for  breath, 
and  it  was  this  movement  of  which  advantage  was 
taken. 

Fig.  185  shows  the  tortoise  moving  about  like  a 
quadruped  in  water,  the  successive  movements  of  the 


264  MOVEMENT 

four  limbs  being  characteristic  of  an  ordinary  walking 
pace.* 

Having  taken  breath,  the  tortoise  returned  to  the 
bi  )ttom  of  the  aquarium  by  a  similar  mode  of  progression. 

With  other  species,  the  marine  turtle,  for  instance, 
there  are  two  distinct  kinds  of  locomotion — firstly,  that 
of  walking,  which  has  just  been  described;  and,  secondly, 
that  which  we  have  compared  to  flying.  In  this  latter 
method  of  progression,  the  hind  limbs  are  stretched  out 
side  by  side,  and  are  free  from  all  movement,  while  the 
fore  limbs  are  moved  backwards  and  forwards  in  the 
execution  of  movements  similar  to  those  of  the  wings 
of  a  "  rowing  "  bird. 

The  progression  of  land  tortoise-;  appeared  to  us  to 

WW**** 

Fig.   185.— Quadrupedal  movements  of  a  fresh-water  tortoise  in  swimming  to  the 

surface. 

resemble  ordinary  walking,  but  not  having  had  time 

to  tame  a  specimen,  we  did  not  succeed  in  inducing  one 

to  walk  in  front  of  the  object-glass;  the  animal,  no  doubt 

frightened  at  the  noise  of  the  apparatus,  obstinately 

kept  its  limbs  tucked  away  under  its  carapace. 

Lizards  are  extremely   difficult  to   deal   with.     To 

place  one  under  favourable  conditions  for  observation 

we  made  use  of  the  circular  canal  which  was  represented 

in   Fig.    50,   and   designed   for   studying    subaqueous 

movements.     The  transparent  part  of  this  canal  was 

lighted  from  beneath,  and  the  photographic  apparatus 

was  placed  at  a  higher  level,  and  received  its  images 

reflected  from  a  mirror  obliquely  inclined  at  an  angle 

*  Sec  sequence  of  these  movements  in  Chap,  xi.,  "  The  Synoptic 
Record  of  Huraes'  Paces." 


COMPARATIVE   LOCOMOTION 


265 


of  45°.  A  lizard  was  placed  on  the  glass  bottom,  and 
silhouetted  on  the  sensitized  plate.  But  grey  or  green 
lizards  were  unable  to  crawl  on  the  slippery  surface  of 
the  glass ;  but,  on  the  other  band,  the  Gecko  with  its 
spatulated  digits  could  run  about  with  ease.     That  all 


Fig.  136.     Grey  lizard.     The  series  must  b^  followed  from  right  to  left 

these  specimens  might  be  under  equally  favourable 
conditions  for  locomotion  a  piece  of  muslin  was  pasted 
on  the  surface  of  the  glass.  This  muslin  should  be 
very  transparent,  and  yet  rough  enough  to  admit  of 


MWW 


j 


Fig.  187.— Gecko.    The  series  must  be  followed  from  left  to  right. 

locomotion.  Figs.  186  and  187  show  the  mode  of  pro- 
gression of  the  grey  lizard  and  the  Gecko.  Taken  as 
a  whole,  the  paces  are  similar,*  but  with  the  Gecko, 

*  See  chap.  xi.     Synoptic  chart  of  the  characteristics  of  the  equine 
trot. 


266 


MOVEMENT 


which  has  a  shorter  body,  the  track  of  the  hind  feet  is 
very  near  that  of  the  front.  Moreover,  the  movements 
are  extensive,  and  cause  a  serpentine  twisting  of  the 
whole  body.  As  these  movements  are  very  rapid,  a 
great  number  of  photographs  must  be  taken — about 
sixty  per  second — in  order  that  their  sequence  may  be 
distinguished. 

Frogs,  Toads,  and  Tadpoles.— In  accordance  with  the 
stage  of  development,  batrachians  depend  on  different 
types  of  locomotion. 

Before  the  tadpole's  legs  are  completely  developed 


Fig.  188. — Locomotion  of  batrachians  at  different  periods  of  development. 


it  swims  with  its  tail  after  the  manner  of  a  fish  (Fig. 
188,  first  row).  When  the  tail  has  disappeared  and 
the  four  legs  are  completely  formed,  the  swimming 
of  batrachians  resembles  that  of  man  (Fig.  188, 
second  row).  The  legs,  which  are  at  first  widely 
separated,  are  brought  suddenly  together,  then  drawn 
up   under    the    body,    and    finally    separated    again, 


COMPAKATIVE   LOCOMOTION 


267 


268  MOVEMENT 

so  as  to  give  a  fresh  impetus  when  they  are  again 
suddenly  approximated.  Meanwhile  the  fore  limbs  are 
pressed  against  the  thorax,  and  appear  to  be  quite 
inactive.*  In  the  intermediate  stage,  when  the  legs 
are  incompletely  developed,  and  the  tail  has  not  yet 
disappeared  (Fig.  188,  third  row),  the  batrachian  has  a 
mixed  mode  of  progression.  Between  the  hind  legs, 
which  execute  the  movements  of  swimming,  the  tail 
keeps  up  an  incessant  wriggling  motion. 

Snakes,  Eels,  Fish. — Snakes  have  a  slightly  different 
method  of  progression  according  as  they  are  on  land 
or  in  water.  An  ordinary  adder  placed  in  the  dry 
canal,  before  described,  executes  undulations  of  con- 
siderable amplitude  (Fig.  189).  As  the  animal  moves 
along,  the  undulations  pass  from  the  anterior  to  the 
posterior  end  of  the  body,  the  same  as  in  the  case  of 
the  swimming  eel.  A  water  adder  placed  in  the  dry 
canal  progresses  in  the  same  manner,  as  also  does  an 
eel.  But  when  these  same  animals  are  placed  in  water, 
they  swim  about  with  an  undulatory  movement  of  less 
amplitude,  but  with  far  greater  regularity.  Fig.  190 
represents  an  eel  in  the  act  of  swimming ;  the  method 
of  progression  is  identically  the  same  as  that  of  the 
adder,  except  that  the  movement  of  the  tail  is  more 
accentuated.  The  tail  of  an  eel  is  transversely 
flattened,  and  imparts  a  movement  like  that  of  other 
fish ;  the  undulations  of  the  tail  are,  however,  more 
pronounced  than  those  of  the  rest  of  the  body. 

Among  other  fish  the  undulations  of  the  body  are 
less  marked,  although  very  noticeable  in  the  case  of  the 
dog-fish,  which  is  a  long-bodied  animal  (Fig.  191).  It  is 
to  be  observed  only  in  the  tail  in  some  species,  the 
movements  of  the  body  being  but  slightly  developed, 
as,  for  example,  is  the  case  with  the  Cyprinidae. 

*  Owing  to  a  mistake  in  the  engraving,  the  order  of  the  images  has 
been  changed  in  several  instances  on  the  second  line  of  figure. 


COMPARATIVE   LOCOMOTION 


269 


19 


270 


MOVEMENT 


Insects  and  Arachnids. — Anions:  six-les;s:ed  insects 
and  eight-legged  arachnids  the  variations  in  the 
methods  of  progression  are  entirely  due  to  the  different 
number  of  legs.  In  these  species  the  separate  legs  of 
each  pair  act  alternately,  and  the  movements  of  one 
pair  alternate  with  those  of  the  next.  It  follows,  as 
was  carefully  observed  by  Carlet  and  M.  de  Moor,* 


Fig.  191. — Dog-fish  swimming. 


that  among  the  Coleoptera,  for  instance  (Fig.  192), 
the  first  and  last  appendages  on  the  same  side  are 
in  contact  with  the  ground,  while  the  middle  one  is 
raised.  On  the  other  side  of  the  body  the  middle 
appendage  is  on  the  ground,  and  the  first  and  last 
ones  raised. 

When  an  insect  turns  round,  the  movements  are 
feebler,  or  cease  altogether,  on  the  side  towards  which 
the  animal  turns. 

In  the  case  of  certain  insects  which  jump  as  well  as 

*  De  Moor  (Archives  de  Biolojie  Liege,  1890).  The  author  gives 
a  very  complete  account  of  his  studies  made  on  the  locomotion  of 
insects.  He  describes  how  he  obtained  the  track  of  each  of  the  feet 
in  different  colours  by  coating  them  with  different  pigments;  the 
insect,  as  it  moved,  left  its  track  on  a  strip  of  paper.  He  also  describes 
how  he  arranged  the  light  so  as  to  best  observe  the  movements. 


COMPARATIVE   LOCOMOTION 


271 


— , 


3% 


"M 


m 


^m 


Wm 


272 


MOVEMENT 


tf- 


,  J 


crawl  we  have  not  been 
able  to  make  out  how 
the  sudden  spring  of  the 
hind  legs  is  effected,  but 
they  crawl  much  in  the 
same  manner  as  Coleop- 
tera,  as  may  be  seen  in 
Fig.  193,  which  repre- 
sents an  orthopterous 
insect. 

Among  the  arachnids 
(Fig.  194)  the  four  feet 
of  each  side  alternate  in 
their  movements,  so 
that  there  are  always  two 
feet  off  and  two  feet  on 
the  ground,  as  can  be 
seen  in  the  case  of  the 
spider. 

To  distinguish  the 
feet  on  the  ground  trom 
those  which  are  raised 
we  illuminated  an  insect 
from  above,  so  that  the 
shadow  of  its  legs  was 
projected  on  to  the  wKite 
surface  upon  which  it 
crawled.  Under  these 
circumstances  the  sha- 
dow of  each  foot  which 
was  in  contact  with  the 
ground  extended  right 
up  to  the  foot  itself;  on 
the  other  hand,  when 
the  foot  was  raised,  a 
gap  existed  between  the 
foot  and  its  shadow. 


COMPARATIVE   LOCOMOTION 


273 


274  MOVEMENT 

Scorpions  move  very  rapidly ;  their  progression  is 
due  to  a  series  of  sudden  springs,  which  can  be  pro- 
voked by  excitation.  The  sequence  of  movements  is 
so  swift  that  we  have  found  it  impossible  to  determine 
their  nature  by  means  of  photography  (Fig.  195). 

All  these  insects  moved  about  on  glass  covered  with 
paper  or  transparent  muslin,  and  were  viewed  by 
translucent  or  reflected  light.  Their  movements  were 
directed  by  means  of  two  sheets  of  glass,  which  were 
arranged  so  as  to  be  parallel  and  vertical,  and  thus  to 
prevent  them  from  leaving  the  desired  track.  These 
few  examples  will  suffice  to  show  how  to  collect  and 
compare  from  various  species  of  animals  chrono- 
photographs  of  different  types  of  locomotion.  In  a 
collection  of  a  great  number  of  photographs  of  this 
kind  one  will  find  the  necessary  elements  for  the 
study  of  comparative  physiology,  a  study  which  we 
mean  to  pursue. 


CHAPTER  XYI 

APPLICATIONS    OF   CHRONOPHOTOGRAPHY   TO 
EXPERIMENTAL    PHYSIOLOGY 

Summary. — Numerous  applications  of  chronophotography ;  it  supple- 
ments the  information  derived  from  the  graphic  method— Study 
of  the  movements  of  the  heart  by  means  of  the  graphic  method — 
Photography  of  the  successive  phases  of  cardiac  action  in  a 
tortoise  under  conditions  of  artificial  circulation — Variations  in 
shape  and  capacity  of  the  auricles  and  ventricles  during  a  cardiac 
cycli — Mechanism  of  cardiac  pulsation  studied  by  means  of 
chronophotography — Comparative  advantages  of  mechanical  and 
chronophotographic  registration — Determination  of  the  centres  of 
movements  in  joints. 

Almost  all  vital  functions  are  accompanied  by  move- 
ment ;  but  any  attempt  to  investigate  them  is  beset 
with  extreme  difficulty,  for  the  majority  of  them  are 
very  complicated  or  very  rapid.  Sometimes,  on  the 
other  hand,  they  are  extremely  slow  and  difficult  to 
observe. 

The  methods  employed  by  physiologists  are  gene- 
rally devised  with  a  view  to  elucidate  what  the  unaided 
eye  cannot  discover  for  itself. 

It  might  reasonably  be  predicted  that  chronopho- 
tography might  be  found  useful  in  this  domain.  It 
might  show,  for  instance,  the  part  played  from  moment 
to  moment  by  the  different  parts  of  the  thorax  in  the 
act  of  respiration.  It  might  follow  the  peristaltic  and 
the  antiperistaltic  contractions  of  the  intestines  through 
all  their  phases  and  under  the  various  conditions  which 
modify  the  characters  of  these  movements.     In  a  word, 


276  MOVEMENT 

it  inight  be  used  in  all  cases  in  which  neither  ordinary 
observation  nor  the  employment  of  the  graphic  method 
could  give  us  any  definite  information. 

There  are  also  many  curious  movements  in  the 
vegetable  kingdom  which  can  be  studied  by  means  of 
chronophotography,  such,  for  instance,  as  the  sudden 
retraction  of  the  leaves  and  petals  of  the  sensitive  plant 
when  touched,  the  gradual  return  of  these  structures 
to  their  original  position,  the  progress  of  vegetable 
growth,  the  unfolding  of  leaves,  and  the  blossoming  of 
flowers. 

Successive  photographs,  taken  at  more  or  less  fre- 
quent intervals  of  time,  will  show  the  various  phases  of 
these  phenomena. 

In  both  kingdoms  the  microscope  reveals  deep  down 
in  the  midst  of  living  tissues  movements  of  immense 
interest,  for  they  are  concerned  with  the  fundamental 
principles  of  organic  life.  Of  such  a  nature  is  the 
circulation  of  blood  corpuscles  in  the  finest  capillaries, 
and  such  is  the  movement  of  the  zoospores  in  the  cells 
of  algae  ;  such  is  the  slow  alteration  in  shape  of  the 
white  corpuscles  of  the  blood,  and  the  phenomenon  of 
phagocytosis,  etc.  It  would  be  a  very  interesting  study 
to  ascertain  the  characters  of  these  movements  by 
means  of  photography. 

To  give  an  instance  of  the  advantages  of  chrono- 
photography as  applied  to  an  experimental  problem  in 
physiology,  we  will  take  the  case  of  cardiac  movements. 
This  is  a  subject  which  has  been  exhaustively  studied 
by  means  of  the  graphic  method;  nevertheless,  chrono- 
photography has  afforded  much  new  information  of 
quite  a  different  kind  ;  we  will  summarize  the  question 
as  it  stands  at  present. 

Analysis  of  Cardiac  Movements  by  means  of  the 
Graphic  Method. — About  thirty  years  ago,  we,  together 
with  our  friend  and  colleague  Chauveau,  suggested  at 


APPLICATIONS   TO  PHYSIOLOGY  277 

the  Academy  of  Science  and  at  the  Academy  of 
Medicine  a  theory  of  cardiac  movement,  based  upon 
information  derived  from  the  graphic  method.  This 
theory,  to-day  universally  accepted,  put  an  end  to 
differences  of  opinion  among  physiologists  and  physi- 
cians, and  it  has  not  been  unassociated  with  recent 
advances  in  the  diagnosis  of  cardiac  and  vascular 
diseases. 

We  were  induced  to  embark  on  these  experiments 
by  the  incomplete  evidence  derived  from  direct  exami- 
nation regarding  the  nature  and  sequence  of  the 
extremely  complicated  movements,  executed  by  the 
heart  from  moment  to  moment  during  a  complete 
cycle  of  events. 

Our  method  was  indirect,  and  consisted  in  register- 
ing the  curves  of  pressure  variations  occurring  in  the 
interior  of  the  cardiac  cavities  as  well  as  outside  these 
chambers.  Our  -curves,  properly  speaking,  did  not 
explain  the  movements  of  the  heart ;  but,  nevertheless, 
they  enabled  us  to  state  the  order  and  sequence  of  the 
auricular  and  ventricular  movements  from  the  changes 
in  pressure  which  they  expressed. 

This  interpretation  was  often  a  very  difficult  task, 
and  required  a  considerable  number  of  experiments  in 
order  to  verify  the  different  points  at  issue.  Although 
it  was  pretty  evident  that  the  maximum  of  pressure  in 
each  cardiac  cavity  corresponded  to  the  moments  at 
which  these  cavities  contracted  for  the  expulsion  of 
the  contained  blood,  yet  it  was  by  no  means  easy  to 
discover  the  significance  of  each  variation  on  the 
cardiography  curves. 

Let  us  examine  tracings  which  express  the 
alterations  in  blood-pressure  in  the  auricles  and 
ventricles,  and  the  phases  of  cardiac  pulsation.  If 
these  figures  were  placed  before  the  eyes  of  a  physician, 
whom  we  will  suppose  ignorant  of  the  physiology  of 


278  MOVEMENT 

the  heart,  he  would  derive  from  the  curves  an  exact 
knowledge  of  the  blood-pressure  obtaining  in  the 
cardiac  chambers,  and  of  the  ever-changing  force  to 
which  the  exploring  apparatus  was  exposed  in  its  con- 
tact with  the  ventricular  walls.  Further,  he  would 
notice  the  exact  sequence  of  these  changes :  but  from 
these  curves  alone  he  would  gain  no  information  con- 
cerning the  organ  which  brought  about  these  changes. 
It  would  be  possible  for  him  to  picture  to  himself  a 
system  of  pistons,  pumps,  and  valves  capable  of  pro- 
ducing similar  results,  but  he  would  never  succeed  in 
realizing  the  actual  shape  of  the  heart  and  the  altera- 
tion in  appearance  and  volume  which  the  different 
cavities  of  this  organ  present  from  moment  to  moment. 

Further,  as  no  analogous  phenomenon  is  to  be  found 
outside  the  animal  kingdom,  the  physician  would 
doubtless  be  at  a  loss  to  understand  the  mechanism 
of  the  ventricular  contractions,  namely,  the  centrifugal 
impulse  given  by  the  organ  at  the  moment  of  systole. 

Even  physiologists  must  acquire  some  preliminary 
knowledge,  by  means  of  vivisection,  of  the  shape  of 
the  heart  and  its  peculiar  movements  before  they  can 
understand  the  real  significance  of  a  cardiogram ; 
but  our  eyes  are  hardly  capable  of  following  the 
rapid  and  complicated  variations  presented  by  a 
heart  in  motion,  the  shape  of  the  various  cavities 
whether  being  filled  or  emptied,  the  moment  of 
distension  of  the  blood-vessels  of  the  heart,  or  the 
contractions  of  the  muscular  fibres,  etc. 

As  soon  as  Ave  had  at  command  a  method  of  chrono- 
photography  which  faithfully  interpreted  the  changes 
in  shape  and  position  of  moving  bodies,  we  sought  to 
derive  from  tins  method  information  supplemental  to 
thai  furnished  by  the  graphic  method.  The  following 
experiments  were  our  first  attempts  in  that  direction. 

Photography  of  the    Successive    Phases   of    Cardiac 


APPLICATIONS   TO  PHYSIOLOGY 


279 


Action  in  a  Tortoise  under  Conditions  of  Artificial  Cir- 
culation.— As  we  had  no  large  animals  at  our  disposal 
in  which  the  movements  of  the  heart  were  accom- 
panied by  such  strange  variations  in  appearance,  we 
were  compelled  to  analyze  the  movements  of  a  land 
tortoise's  heart  by  means  of  chronophotography. 

In  order  that  the  entire  heart  might  be  visible,  we 
removed  it  from  the  body  and  placed  it  under  con- 
ditions of  artificial  circula- 
tion.* Then,  in  order  that 
the  various  parts  of  the  cir- 
culatory apparatus  might  be 
confined  to  as  narrow  limits 
as  possible,  the  apparatus 
was  simplified  as  represented 
in  Fig.  196. 

The  narrow  end  of  a  glass 
funnel  was  introduced  into 
the  vena  cave  close  up  to 
the  left  auricle,  and  fixed 
there  by  a  strong  ligature. 
Then  a  glass  canula  was 
introduced  into  the  aorta, 
and  connected  with  a  piece 
of  indiarubber  tubing  to  re- 
present the  artery  ;  this  tub- 
ing in  turn  was  connected 
with  a  piece  of  glass  tubing 
bent  at  an  angle  (o),  the 
opening  of  the  latter  was 
directly     above     the     glass 

funnel.  The  whole  of  the  apparatus  was  placed  on  a 
solid  support,  and  allowed  to  stand  out  in  relief  against 
a  light  background. 

*  For  the  description  of  the  method,  see  Marey,  La  Circulation  du 
sang  a.  Veiat  Piiysiologique  et  dans  les  Maladies,  p.  70,  Fig.  28.  Paris, 
G.  Masson,  1881. 


Fig.  196. — Heart  of  a  tortoise  ui;der 
conditions  of  artificial  circulation, 
a,  auricle  ;  »,  ventricle;  a.  t.,  arterial 
tube;  o,  outflow;  s,  support  of  the 
funnel,  which  represents  the  venous 
system  and  its  communication  with 
auricle. 


280  MOVEMENT 

Some  defibrinatecl  bullock's  blood  was  poured  into 
the  funnel  so  as  to  fill  it  three  parts  full.  After  a  few 
minutes,  the  blood  was  seen  to  fill  the  auricle,  and  then 
almost  immediately  to  be  discharged  into  the  ventricle  ; 
the  latter,  in  its  turn,  contracted  and  sent  its  contents 
through  the  tube,  from  which  it  was  emptied  into 
the  funnel  through  the  attached  pipe. 

Instead  of  the  weak  and  occasional  movements 
executed  by  the  heart  when  depleted  of  blood,  an 
energetic  circulation  was  established,  and  continued 
from  six  to  ten  hours,  and  sometimes  even  longer,  the 
time  being  dependent  on  the  season  of  the  year. 
Under  the  influence  of  the  heart's  activity,  the  blood 
soon  assumed  a  veinous  character,  and  therefore  it  was 
found  essential  to  renew  it  from  time  to  time,  in 
order  that  the  energy  of  the  artificial  circulation 
might  be  maintained. 

The  photographs  thus  obtained  can  only  be  repre- 
sented as  shadows,  because  the  red  colouration  of  the 
tortoise's  heart  is  not  photogenic,  and  cannot,  therefore, 
form  an  image  by  reflection,  and  give  the  configuration 
which  is  necessary  for  understanding  the  changes  in 
form  of  the  auricles  and  ventricles,  which  occur  from 
moment  to  moment. 

These  silhouettes,  however,  enable  one  to  follow  the 
various  stages  by  which  the  blood  circulates  through 
the  heart,  and  the  tubes  which  communicate  with  the 
cavities  of  that  organ.  As  the  photograph  represented 
in  Fig.  197  has  to  contain  several  images,  we  re- 
duced as  far  as  possible  the  component  parts  of  the 
apparatus  for  carrying  on  the  artificial  circulation. 
The  broad  funnel  in  Fig.  196  has  been  replaced  by 
a  thick  glass  tube  pointed  at  the  end,  so  as  to  pass 
through  the  vein  and  gain  entrance  to  the  auricle. 
This  constitutes  the  veinous  reservoir.  Another  and 
finer  tube,  representing  the  artery,  fits  into  the  orifice 


APPLICATIONS   TO  PHYSIOLOGY  281 

of  the  aorta,  and  curves  round,  so  as  to  pour  its 
contents  into  the  veinous  reservoir. 

In  following  the  chronophotographic  images  which 
correspond  to  the  successive  phases  of  the  cardiac  cycle, 
the  series  must  be  read  from  left  to  right.  It  will  be 
noticed  at  once  that  in  the  first  position  no  blood  is 
passing  into  the  veinous  reservoir  through  the  arterial 
tube,  the  ventricle  is  consequently  relaxed  (diastole). 

The  positions,  2,  3,  4,  and  5,  show  a  jet  of  blood 
flowing  into  the  reservoir,  the  ventricle  is  therefore 


FrG.  197.— Seven  success  ve  photographs  of  a  tortoise's  heart  with  artificial  circula- 
tion. The  series  must  be  read  from  left  to  right.  They  are  taken  at  intervals 
of  ^j  of  a  second.  In  each  member  of  the  series  the  auricle  is  on  the  left  and  the 
ventricle  on  the  right.  From  the  2nd  to  the  5th  image  the  ventricular  systole  may 
be  recognized  by  tiie  stream  ot  blood  which  \  ours  into  the  venous  reservoir. 

contracted  (systole).  Finally,  positions  6  and  7, 
in  which  the  jet  of  blood  can  no  longer  be  seen, 
represents  a  fresh  diastolic  period.  The  same  phe- 
nomena continue  indefinitely,  and  pursue  the  same 
sequence  of  events  as  already  described. 

The  series  of  positions  might,  therefore,  be  transposed, 
with  No.  1  immediately  following  No.  7. 

As  for  the  heart,  nothing  but  the  contour  can  be 
seen,  and  this  indicates  the  alternate  dilatations  and 
contractions  of  the  auricle  and  ventricle. 


282  MOVEMENT 

The  auricle,  which  commences  to  fill  in  the  2nd 
position  of  the  series,  is  in  process  of  contraction 
during  the  6th,  7th,  and  1st.  Now,  during  the  stage 
of  auricular  contraction,  the  ventricle  may  be  seen 
gradually  rilling,  so  that  in  position  1,  when  the 
auricle  has  reached  the  climax  of  its  contraction,  the 
ventricle  has  attained  to  its  maximum  of  repletion. 
The  alternations  between  the  diastolic  and  systolic 
periods  of  the  two  chambers  of  the  heart  are  therefore 
perfect. 

The  duration  of  these  phases  can  be  calculated 
almost  exactly  from  the  number  of  positions  which 
correspond  to  each  stage.  The  apparatus  produced 
10  images  per  second,  and  since  7  images  sufficed 
to  rejDresent  an  entire  cardiac  cycle,  the  latter 
may  be  concluded  to  last  -j7g  of  a  second.  In 
the  same  way  to  the  systole  of  the  ventricles  may 
be  assigned  a  duration  of  ^0  of  a  second,  and  to  the 
diastole  ^*. 

These  primary  notes  on  the  changes  in  shape  of  the 
cavities  of  the  heart  will  be  supplemented  by  the 
following  experiment. 

Variations  in  Shape  and  Capacity  of  the  Auric  es  and 
Ventricles  during  a  Cardiac  Cycle. — The  surface  of  the 
heart  can  be  rendered  photogenic  by  means  of  a  very 
simple  device ;  it  suffices  to  paint  it  with  rather  a  thick 
coat  of  Chinese  white.  The  heart  being  rendered  thus 
quite  white,  the  play  of  light  and  shade  displays  the 
alterations  in  shape  and  capacity  of  the  different 
cavities.     If  a  chronophotograph  be  taken  of  such   a 

*  These  measurements  do  not  pretend  to  rival  in  exactness  those 
derived  from  the  graphic  method,  which  are  almost  infinitely  accurate. 
When  the  commencement  and  termination  of  a  phenomenon  is 
measured  by  means  of  a  discontinuous  serie9  of  images,  there  may  be 
an  error  us  regards  both  these  stages.  The  commencement  and 
termination  may  occur  between  two  exposures  of  the  photographic 
plate,  and  it  is  impossible  to  say  exactly  when  they  occur. 


APPLICATIONS  TO   PHYSIOLOGY 


283 


Fig.  198. 

On  observing  the  series  from  above 
downwards,  the  following  phenomena 
are  observed :  — 

1.  The  ventricle,  v,  has  completed 
its  systole,  and  has  diminished  in 
volume.  The  auricle,  a,  is  full,  en- 
larged, and  shiny. 

2.  The  auricle  has  commenced  to 
empty  itself  and  change  its  form ; 
its  external  surface  is  flattened,  and 
exhibits  two  irregular  borders  and  a 
roundedextremity,givingit  a  tongue- 
like appearance.  The  ventricle  is 
beginning  to  enlarge. 

3.  The  auricle  has  diminished  in 
size,  and  the  extremity  is  approach- 
ing the  ventricle;  the  latter  is  be- 
coming still  larger. 

4.  The  auricle  is  still  contracting, 
and  the  ventricle  is  approaching  its 
maximum  of  repletion. 

5.  The  auricle  has  completely 
emptied  itself,  and  the  ventricle  is 
diminished  in  volume ;  its  systole 
is  commencing  (at  this  moment  the 
blood  is  being  poured  into  the  re- 
servoir). 

6.  The  ventricular  systole  con- 
tinues, and  the  relaxed  auricle  com- 
mences to  fill. 

7.  The  ventricular  systole  is  com- 
pleted, the  auricle  is  distended  and 
shiny,  and  the  phase  represented  in 
the  first  of  the  series  is  repeated. 


ft 


284  MOVEMENT 

heart,  which,  for  convenience'  sake,  should  not  be 
obscured  by  complicated  apparatus,  it  will  give  a  series 
of  positions  which  may  be  studied  in  detail.  Some  of 
the  most  important  points  learnt  from  examining  such 
a  series  are  as  follows  : — The  cavities  of  the  heart  have 
each  their  peculiar  shape,  and  as  the  blood  pours  in, 
they  do  not  assume  such  a  rotund  appearance  as  would 
be  presented  by  a  homogeneous  and  elastic  sac,  but 
take  on  various  forms,  apparently  conditioned  by  the 
unelastic  nature  of  the  pericardium,  by  which  the 
auricles  and  ventricles  are  confined,  and  generally 
compressed.  Consequently,  the  outer  surface  of  these 
cavities  appears  convex,  and  moulded  to  the  concavity 
of  the  pericardial  sac.  The  adjacent  sides  of  the 
chambers  are  flattened  against  one  another,  producing 
facets  and  more  or  less  uneven  ridges.  The  facets 
are  not  always  equally  visible :  on  the  ventricle,  for 
instance,  only  one  facet  can  be  distinctly  seen  just  at 
the  moment  when  it  is  uncovered  by  the  increasing 
contraction  of  the  auricle.  These  distinctions  are 
gradually  effaced  during  the  systole.  The  ventricles 
then  become  speroidal  in  shape,  proving  that  all 
sections  of  the  wall  contribute  an  equal  share  in  the 
compression  of  the  contained  blood. 

Another  fact,  which  such  a  series  of  photographs 
teaches  us,  is  that  the  diastole  of  the  ventricles  coin- 
cides exactly  with  the  systole  of  the  auricles.  The 
filling  of  the  ventricle  depends,  so  to  speak,  on  the 
auricular  systole. 

We  recommend  an  examination  of  such  a  series  to 
those  who  still  believe  in  an  active  diastole— a  sort  of 
aspiration  of  the  blood  by  the  ventricles — a  strange 
belief,  not  to  be  explained  by  the  structure  of  the 
heart,  and  which  the  action  of  the  auricles  renders 
perfectly  useless. 

Mechanism  of  Cardiac  Pulsation  studied  by  means  of 


APPLICATIONS  TO  PHYSIOLOGY  285 

Chronophctography. — We  have  already  explained  this 
phenomenon  as  due  to  the  sudden  hardening  of  the 
ventricles,  which,  although  relaxed  and  tensionless 
during  the  stage  of  passive  filling,  become  more  or  less 
spherical  and  hard  when  active  contraction  begins, 
they  then  actually  exercise  pressure  on  the  blood 
which  has  previously  distended  them.  This  theory 
alone  accounts  for  all  the  phenomena  which  can 
be  observed;  it  explains  why  the  pulsation  of  the 
heart  is  perceptible  at  all  points  of  the  surface  of 
the  ventricle,  it  renders  the  fact  intelligible,  which 
appears  at  first  paradoxical,  namely,  that  the  heart 
presses  against  the  thoracic  parietes,  not  when  it 
expands,  but  when  it  diminishes  in  volume.  It  is 
not  by  an  alteration  in  volume,  but  by  an  alteration  in 
hardness,  that  the  heart  repels  everything  that  has 
a  tendency  to  compress  it.  The  maximum  degree  of 
hardness  corresponds,  as  we  before  mentioned,  to  the 
systole  of  the  ventricles,  namely,  at  the  moment  when 
their  powerful  muscular  fibres  compress  the  blood  and 
project  it  into  the  arterial  system. 

Such  is  the  mechanism  which  causes  the  sudden 
pulse  which  feels  like  a  shock  to  the  finger,  and  which 
we  call  the  pulsation,  to  suggest  an  analogy  between 
it  and  the  pulse  at  the  wrist ;  that  it  consists  of  a 
sudden  rise  in  tension  in  the  organ  can  be  proved 
by  touching  its  hardened  surface  with  the  finger. 

This  theory  becomes  more  intelligible  if  the  ventricles 
of  a  large  animal  are  held  in  the  hand ;  if  they  are 
compressed  by  the  fingers,  there  is  a  distinct  sense  of 
resistance  at  the  moment  when  the  surface  of  the  heart 
is  made  tense,  which  intimates  that  the  systolic 
contraction  of  the  muscular  fibres  is  in  process. 

We  endeavoured  to  render  this  phenomenon  visible 
to  the  eye  by  the  following  experiment,  in  which  we 
made  use  of  an  arrangement  of  this  kind.  The 
20 


286 


MOVEMENT 


apparatus,  as  depicted  in  Fig.  197,  for  carrying  on  an 
artificial  circulation,  was  employed ;  but  the  whole  of 
it  was  obliquely  inclined  and  secured  to  a  bevelled 
cork  by  means  of  modelling  wax.  The  heart,  Fig.  199, 
was  then  placed  on  a  horizontal  stand  resting  on  one 
of  its  surfaces,  while  the  other  was  freely  exposed  to 
view,  so  that  the  pulsation  might  be  examined. 

To  prove  our  point,  it  must  be  shown  that,  when 
a  solid  body  is  pressed  against  the  ventricular  wall 
with  a  certain  amount  of  force,  the  latter,  during  a 
condition  of  relaxation,  is  indented,  and  allows  the 
solid  body  to  sink  into  the  hollow  thus  formed  ;  and 


Fig.  199.— Experiment  for  showing  by  chronophotography  the  mechanism  of  cardiac 
pulsation. 


that,  on  the  other  hand,  during  systole,  the  ventricles 
repel  this  body,  and  efface  the  depression. 

For  this  purpose  a  small  square  of  cork  (M,  image 
2)  is  allowed  to  rest  on  the  surface  of  the  ventricles, 
and  a  lever  with  a  counterpoising  disc  is  balanced  on 
the  cork.  The  ventricle  receives  an  indentation  from 
the  external  pressure,  and  the  cork  partially  disappears 
within  the  depression,  as  shown  in  the  first  position  of 
Fig.  199. 

This  is  because  the  diastole  of  the  ventricles  is  in 
process  of  operation,  as  may  be  recognized  by  the 
absence  of  the  jet  of  arterial  blood.      In  position   2 


APPLICATIONS   TO   PHYSIOLOGY  287 

of  the  same  figure,  the  ventricle  is  in  systolic  contrac- 
tion, which  is  evident  by  the  flow  of  blood  into  the 
reservoir.  Xow,  at  this  moment  the  entire  square  of 
cork  comes  into  view,  expelled  from  the  depression 
into  which  it  had  sunk  when  the  ventricle  was 
relaxed. 

Comparative  Advantages  of  Mechanical  and  Chrono- 
photographic  Registration. — To  continue,  these  experi- 
ments, which  constitute  some  of  the  first  applications 
of  chronophotography  to  experimental  physiology, 
give  additional  information  concerning  the  functions 
of  the  heart  over  and  above  that  derived  from  ordinary 
cardiography.  In  comparing  the  two  methods,  it  will 
be  seen  that  they  attain  different  ends.  The  one  by 
means  of  variations  in  a  curve  expresses  the  minutest 
changes  in  blood-pressure  that  occur  in  the  cardiac 
chambers,  and  indirectly  this  reveals  the  smallest 
details  of  cardiac  function.  But  this  method  only 
appeals  to  the  initiated ;  it  requires  numerous  control 
experiments  so  that  one  may  fully  understand  the 
meaning  of  the  cardiogram.  The  other  method,  strictly 
speaking,  is  the  direct  examination  of  the  movements 
of  the  heart  by  a  more  subtle  eye  than  ours,  and  one 
that  is  capable  of  grasping  in  a  moment  the  sum  total 
of  the  changes  which  take  place  in  the  different 
cavities  of  the  heart.  The  information  to  be  derived 
from  this  method  is  self-evident.  The  comparison  of 
a  series  of  consecutive  images  also  affords  an  oppor- 
tunity of  observing  every  visible  phase  of  the 
phenomenon.  It  affords  us  no  information,  as  does 
the  cardiogram,  concerning  the  energy  which  primarily 
conduces  to  the  changes  in  form  ;  in  fact,  it  only  gives 
an  approximate  idea  of  the  sequence  of  the  various 
phases  of  movement,  because  its  record  is  one  of 
intermittent  indications,  instead  of  the  continuous 
record  of  a  curve.     Nevertheless,  important  discoveries 


288  MOVEMENT 

in  the  realm  of  physiology  may  be  looked  for  from 
chronophotography. 

Movements  which,  in  the  case  of  the  small  heart  of 
a  tortoise,  have  only  been  sketched  in  outline,  should 
be  more  fully  studied  in  the  case  of  large-sized  tortoises, 
for  the  photographs  would  be  larger  and  more  instruc- 
tive. Better  still  to  operate  on  the  heart  of  large 
mammals,  proceeding  in  the  orthodox  manner  by 
opening  the  thorax  and  inducing  artificial  respiration. 
If  the  heart  then  be  whitened  as  before  described,  and 
a  strong  beam  of  light  directed  on  the  organ,  photo- 
graphs can  be  taken  containing  details  not  to  be  found 
when  the  hearts  of  small  animals  are  employed.  For 
instance,  one  may  observe  the  prominence  caused  by 
arteries  and  veins,  the  muscular  fasciculi,  the  folds  of 
the  serous  membranes,  and  the  displacements  of  the 
heart  within  the  cavity  of  the  pericardium,  etc. 

The  effects  of  electrical  or  other  excitation  applied 
to  the  different  points  of  the  surface  of  the  heart  can 
be  estimated  with  extreme  precision.  Graphic  regis- 
tration and  chronophotography  give,  therefore,  very 
different  kinds  of  information  concerning  the  heart, 
but  both  are  equally  useful.  Just  as  auscultation  and 
percussion,  though  they  greatly  differ,  nevertheless 
contribute  with  equal  efficiency  towards  the  diagnosis 
of  the  physical  condition  and  the  functional  adequacy 
of  the  heart. 

One  could  indefinitely  multiply  examples  of  the 
various  applications  of  this  new  method  to  experi- 
mental physiology.  We  have  already  mentioned  a 
few  in  passing  ;  but  chronophotography  enables  us  to 
determine  the  function  proper  to  each  muscle  in  the 
act  of  locomotion,  by  observing  the  prominence  caused 
by  the  muscle  in  contracting  during  the  various  phases 
of  the  movement. 

But  if  there   is   one   question   more   obscure   than 


APPLICATIONS   TO   PHYSIOLOGY  259 

another,  it  is  the  determination  of  the  centres  of 
movement  of  a  joint. 

Determination  of  the  Centres  of  Movement  in 
Joints. — When  two  articular  surfaces  move  on  one 
another,  the  movement  does  not  always  take  place 
round  a  point  corresponding  to  the  centre  of  curvature 
of  the  surfaces.  We  know,  for  instance,  that  in  the 
case  of  the  knee-joint  the  condyles  of  the  femur 
simultaneously  rotate  and  slide  on  the  articular 
surfaces  of  the  tibia,  and  that  the  condyles  of  the 
lower  jaw  slide  in  various  directions  in  the  glenoid 
cavity  of  the  temporal  bone,  etc.  It  must  follow, 
therefore,  that  the  centre  of  articular  movement  is 
not  indicated  by  the  anatomical  relations,  but  must 
be  empirically  discovered. 

This  problem  is  almost  identical  with  that  which  is 
disposed  of  in  regard  to  the  rolling  of  ships,  and  the 
same  means  may  be  employed  for  the  experimental 
solution.  On  the  cadaver  the  matter  is  simple :  a 
hole  is  drilled  in  the  condyle  of  the  inferior  maxilla, 
and  another  in  the  ascending  process  of  the  same 
bone  near  the  lower  extremity.  A  polished  metal 
wire  is  stretched  between  these  two  points  ;  in  the 
photograph  it  will  be  represented  as  a  bright  line 
indicating  the  axis  of  the  ascending  portion  of  the 
inferior  maxilla. 

The  skin  of  the  subject  is  slightly  blackened,  and 
a  series  of  photographs  taken  on  a  hxed  plate  while 
the  jaw  is  worked  up  and  down.  The  lines  stand  out 
clearly  in  the  photograph,  and  cross  each  other  at 
the  points  which  represent  the  temporary  centres  of 
movement  of  the  bone  during  its  angular  displacements. 

On  the  living  subject  the  experiment  is  not  much 
more  difficult,  A  small  "  planchette  "  applied  to  the 
teeth  of  the  lower  jaw  is  kept  in  position  by  elastic 
bands  passing  under  the  chin.     Into  this  "  planchette," 


290  MOVEMENT 

which  follows  all  the  movements  of  the  bone,  a  bright 
metallic  wire  is  fixed,  and  bent  in  such  a  manner  as 
to  correspond  to  the  angle  of  the  jaw;  it  is  cut  off 
short  at  the  level  of  the  condyles. 

All  the  maxillary  movements  are  reproduced  by  the 
wire,  the  upright  end  of  which  indicates  by  its  inter- 
sections on  the  photograph  the  centres  of  articular 
movement. 

The  applications  of  chronophotography  for  analyzing 
such  movements  as  occur  within  the  field  of  the  micro- 
scope will  probably  be  of  great  importance.  Our 
efforts  in  this  direction  will  be  recounted  in  the  follow- 
ing chapter. 


CHAPTEK  XVII 

MICROSCOPIC   CHRONOPIJOTOGRAPHY 

Summary. — Various  movements  observable  within  the  field  of  the 
micro.-eope — Applications  of  chronophotography  to  the  study  of 
these  movements — Difficulties  of  the  subject — Special  arrange- 
ment  of  the  apparatus  for  ehronophctography  on  fixed  plates  and 
on  moving  films — Retraction  of  the  stalk  in  vorticella — Move- 
ment of  the  blood  in  capillary  vessels — Movements  of  the  zoo- 
spores in  the  cells  of  conferva — The  use  of  the  solar  microscope 
in  chronophotography — The  easy  application  of  this  method. 

The  microscope  has  been  found  of  use  in  all  branches 
of  natural  science,  and  by  it  the  observer  can  fathom 
the  minutest  structural  details  of  an  organ,  and  can 
study  in  certain  of  their  component  cells  movements 
which  are  the  very  essence  of  their  activity. 

Although  Harvey,  by  a  flight  of  genius,  concluded 
that  arterial  blood  returned  in  some  sort  of  way  by 
the  veins,  the  actual  demonstration  of  this  passage 
was  not  effected  until  the  invention  of  the  microscope. 
The  whole  secret  was  then  suddenly  revealed  to  the 
astonished  eyes  of  Jlalpighi — the  presence  of  corpuscles 
in  the  plasma  of  the  blood,  the  capillary  ramifications 
of  the  vessels  which  contained  it,  and  the  vagarious 
current  which  left  the  arteries  and  effected  its  return 
by  way  of  the  veins. 

The  contraction  of  muscles  was  inexplicable  until 
the  use  of  the  microscope  revealed  the  existence  of 
muscular  fibres,  their  shortening  by  means  of  an 
aggregation  of  the  component   discs,  and   the  wave 


292  MOVEMENT 

that  travelled  along  the  length  of  the  fibre  during 
the  act  of  contraction.  Since  that  time  physiologists 
have  no  longer  gone  astray  after  hypothetical  "veins"; 
it  is  in  the  actual  fibres  of  the  muscles  that  they  seek 
the  origin  of  mechanical  energy  in  animals. 

Facts  accumulate — little  by  little  the  theory  un- 
folds itself,  and  the  moment  is  felt  to  be  fast 
approaching  when  muscular  contraction  will  be  a  fully 
explained  fact. 

The  microscope  shows  us  in  a  drop  of  water  the 
animate  motion  of  a  million  minute  organisms  roaming 
about  with  curious  modes  of  locomotion — methods 
which  find  no  counterpart  among  the  more  highly 
developed  animals. 

The  pulsation  of  the  heart  can  be  seen  through  the 
transparent  integuments  of  certain  larvae ;  so,  too,  can 
the  contraction  of  the  intestine,  the  curious  phenomena 
connected  with  generation,  and  the  slow  metamorphosis 
of  the  ovum  or  the  embryo. 

The  chemist  himself,  as  he  watches  the  beautiful 
crystalline  arborizations  developing  upon  the  micro- 
scopic slide,  essays  to  interpret  the  laws  of  this 
mysterious  architecture. 

All  these  movements,  however  slow  or  however  rapid 
be  the  process,  can  be  followed  in  their  respective 
phases  by  means  of  successive  photographs,  no  less 
clearly  than  they  can  be  viewed  under  the  microscope. 

Applications  of  Chronophotography  to  the  Study  of 
these  Movements  within  the  Field  of  this  Microscope. — 
Our  own  instrument  is  the  only  one  up  till  now  which 
can  be  used  for  taking  a  photographic  series  of  micro- 
scopical objects.  Since  our  instrument  is  only  pro- 
vided with  one  object-glass,  the  latter  must  be  of 
suitable  focal  length  for  forming  images  on  the 
sensitized  plate  of  such  a  nature  that  they  can  be 
enlarged  to  any  degree.     The  process  of  microphoto- 


MICROSCOPIC   CHRONOPHOTOGRAPHY  293 

graphy  has  of  late  years  been  brought  to  a  high 
standard  of  perfection,  and  apparently  at  the  present 
time  it  is  only  necessary  to  follow  the  rules  laid  down 
i:i  the  various  treatises  on  the  subject.  In  the  practical 
application,  however,  difficulties  arise  the  causes  of 
which  are  not  far  to  seek.  They  consist  principally 
in  the  illumination  of  the  object. 

Very  small  organisms  generally  move  at  a  rate 
quite  disproportionate  to  their  size.  Infusoria  cross 
the  field  of  the  microscope  in  a  moment,  and  execute 
an  immense  number  of  movements  which  the  eye 
cannot  follow.  The  vibrating  cilia,  for  instance,  which 
serve  as  locomotor  appendages  in  many  of  these 
animalcules,  vibrate  with  such  rapidity  that  they  are 
absolutely  invisible,  and  only  come  into  view  when 
the  animals  are  dead. 

To  obtain,  therefore,  distinct  photographs  of  these 
movements,  the  exposure  must  be  extremely  short, 
We  have  already  learned  that,  to  obtain  photographs 
of  the  wings  of  an  insect  during  flight,  the  exposure 
must  be  reduced  to  gsooo*  Part  oi  a  seconc^  an(^  that, 
too,  under  conditions  of  brilliant  illumination  ;  in 
fact  the  insects  were  photographed  in  silhouette 
against  the  disc  of  the  sun  itself.  For  microscopic 
creatures,  even  this  illumination  would  be  altogether 
inadequate,  in  view  of  the  extremely  short  exposure 
necessitated  by  the  rapidity  of  their  movements.  Ft 
is  no  longer  possible  to  photograph  the  object  to 
actual  scale,  it  must  be  enormously  magnified,  and 
this  magnification  entails  a  corresponding  diminution 
of  the  light  which  reaches  the  sensitized  plate. 

A  linear  magnification  of  100  diameters  reduces 
ten  thousand-fold  the  intensity  of  the  light  dis- 
tributed over  the  plate. 

It  is  true  that  with  powerful  lenses  the  solar  rays 
can  be  sufficiently  condensed,  but  then  the  heat  which 


294  MOVEMENT 

accompanies  this  light  would  soon  destroy  the  living 
creatures  which  move  about  in  the  preparation.  The 
employment  of  vessels  containing  a  solution  of  glycerine 
and  alum  has  been  regarded  as  the  best  means  of 
arresting  caloric  rays  ;  it  is,  however,  altogether  in- 
efficient, and  so  we  have  resorted  to  a  special  arrange- 
ment of  our  own.  Instead  of  allowing  the  light  to 
shine  continuously  on  the  preparation,  it  was  projected 
in  an  intermittent  fashion,  and  only  allowed  to  act  for 
a  very  short  duration,  generally  less  than  xoVo  Par^  °f 
a  second. 

By  this  method,  no  matter  how  great  the  condensa- 
tion of  the  heat,  it  could  never  inflict  an  injury  on 
the  creatures  under  observation. 

Chronophotography  lends  itself  most  happily  to 
these  instantaneous  illuminations. 

It  is  quite  sufficient  to  place  the  object  under 
examination  behind  the  circular  diaphragms.  The 
function  of  those  discs  from  that  time  forward  is  to 
intercept  the  luminous  rays,  which  would  otherwise 
reach  the  preparation,  and  only  to  illuminate  the 
latter  during  the  short  intervals  when  the  fenestra- 
tions in  the  two  diaphragms  coincide. 

Fig.  200  shows  the  principal  parts  of  the  special 
apparatus  which  is  adapted  to  the  chronophotographic 
camera  for  the  analysis  of  microscopic  movements. 

A  wooden  box  with  a  central  aperture  slides  into 
the  front  part  of  the  apparatus  like  the  frame  for 
containing  the  object-glasses  which  has  already  been 
described. 

This  box  contains  an  object-glass,  C,  in  its  anterior 
portion  for  condensing  the  light  which  reaches  it  from 
the  heliostat.  The  focus  of  this  condenser  is  arranged 
so  as  to  fall  upon  the  plate  p,  at  the  same  spot  at 
which  the  preparation  is  to  be  placed.  During  the 
process  of  focussing,  the  position  of  the  plate  carrier 


MICROSCOPIC  CHROXOPHOTOGRAPHY  295 

is  the  first  to  be  arranged,  and  this  is  carried  out  by 
means  of  the  knob  B,  which  controls  a  rack,  and  finally 
by  the  long  rod  mv,  which  turns  a  micrometer  screw. 

The  microscopic  object-glass  0  is  then  brought  to 
bear  upon  the  preparation. 

The  rays  from  the  object  then  cross  a  square  metallic 


Fig.  200.— Special  apparatus  adapted  to  cbronophotography  for  studying  the  move- 
ments of  microscopic  specimens. 

box  behind  the  lens,  and  finally  traversing  the  wooden 
box,  and  the  bellows  attached,  reach  the  ground  glass 
of  the  image  chamber.* 

From  the  side  of  the  metallic  box  the  tube  of  a 
microscope  runs  obliquely,  and  is  provided  with  an 
ordinary  eye-piece.  By  an  arrangement  invented  by 
M.  Xachet,  the  image  can  be  projected  either  on  to 

*  For  the  description  of  this  chamber  refer  back  to  p.  116,  Fig.  80. 


296  MOVEMENT 

the  ground  glass  or  along  the  tube  of  the  microscope 
according  as  desired.  This  arrangement  consists  of 
a  refracting  prism,  which  is  set  in  motion  by  the 
knob  P. 

On  pressing  this  knob,  the  prism  is  brought  into 
play,  and  the  image  of  the  preparation  is  projected 
along  the  tube  of  the  microscope  ;  on  pulling  the  knob 
out,  the  prism  is  removed  and  the  image  falls  directly 
upon  the  ground  glass  or  upon  the  sensitized  plate. 

As  it  would  be  impossible  to  search  for  interesting 
parts  of  the  preparation  from  behind  the  apparatus 
by  watching  the  image  upon  the  ground  glass,  this 
portion  of  the  operation  is  effected  by  looking  through 
the  eye-piece  of  the  obliquely  placed  microscope.  The 
eye-piece  can  be  adjusted  by  means  of  a  correcting 
lens,  in  such  a  way  that  the  image  is  always  in  focus 
on  the  sensitive  plate  when  it  is  in  focus  as  viewed 
through  the  eye-piece.  The  focussing  is  carried  out 
as  follows,  a  screen  of  fairly  thick  paper  is  placed  in 
front  of  the  condenser  so  that  the  light  passing  through 
it  does  not  heat  the  preparation,  and  at  the  same  time 
the  eye  applied  to  the  microscope  can  easily  stand  the 
illumination.* 

When  the  process  of  focussing  is  complete  and  the 
movements  are  ascertained  to  be  under  favourable 
conditions,  the  circular  diaphragms  are  rotated  so  as 
to  obstruct  the  continuous  light,  the  screen  is  removed, 
the  prism  drawn  away,  and  the  camera  set  in  order 
for  taking  a  photograph.  In  this  case,  as  in  the  other 
experiments  described,  it  is  as  well,  to  take  some 
photographs  on  fixed  plates.  The  moving  object 
must  be  strongly  illuminated  in  front  of  a  dark 
background.      For    slight    degrees   of    magnification 

*  It  would  be  very  imprudent  not  to  use  the  screen,  and  care  should 
l»i-  taken  that  it  is  not  removed  during  the  process  of  focussinir;  the 
blinding  light  which  might  otherwise  strike  the  retina  would  be 
attended  with  grave  consequences. 


MICROSCOPIC  CHRO^OPHOTOGRAPHY  297 

M.  Xachet  has  constructed  a  condenser  in  the  form  of 
a  cone  with  a  spheroidal  base.  This  base  is  hollowed 
out  in  the  middle  for  the  reception  of  a  capsule  con- 
taining thick  black  varnish.  If  the  light  is  thrown 
on  the  apex  of  this  cone,  it  will  be  reflected  in  the 
form  of  converging  rays,  and  illuminate  the  objects 
contained  in  the  preparation,  Avhich  consequently 
stand  out  clearly  against  the  dark  central  background. 
But  this  arrangement  is  only  applicable  when  the 
magnifying  power  is  low,  and  has  not  up  to  the 
present  produced  any  very  interesting  results.  Yet 
we  do  not  desjDair  of  obtaining  by  some  other  means 
a  good  series  of  photographs  on  a  dark  background, 
and  with  fixed  plates. 

Chronophotography  on  moving  plates  is  of  far  easier 
application,  and  the  first  object  submitted  by  us  to 
this  method  of  observation  was  a  vortieella  in  active 
movement.  This  species  of  infusoria  is  shaped  some- 
thing like  a  funnel,  and  is  beset  with  a  crown  of 
vibrating  cilia.  It  is  supported  on  a  spirally  twisted 
stalk  which  is  attached  by  its  other  extremity  to 
some  vegetable  fibre,  and  furnishes  a  fixed  point  of 
support. 

From  time  to  time  the  stalk  executes  sudden  re- 
tractions by  approximating  the  turns  of  the  spiral, 
and  the  funnel-shaped  bell  is  suddenly  brought  up  to 
the  point  of  attachment.  The  stalk  then  lengthens 
out,  and  the  spiral  arrangement  disappears  until  the 
following  retraction. 

Fig.  201  shows,  under  a  considerable  degree  of 
magnification,  several  of  these  vorticellae  in  the  midst 
of  a  tangle  of  conferva  filaments. 

To  follow  the  movement  more  easily  it  is  as  well  to 
take  as  a  guide  some  fixed  point  such  as  the  intersec- 
tion of  two  filaments  selected  from  the  network  in  the 
field  of  the  microscope.     For  instance,  in  the  figure 


298 


MOVEMENT 


before  us,  in  the  upper  half  of  the  left-hand  side, 
there  is  an  irregular  rectangle,  and  in  this  there  are  two 
vorticellse  of  unequal  size.  The  larger  of  them,  or 
that  on  the  left,  is  situated  at  about  the  same  level  as  the 
other ;  in  the  following  illustrations  it  gradually  sinks 
lower  down  in  the  field  of  the  photograph,  while  the 
turns  of  the  spiral  appear  more  closely  approximated. 


{ i  n    mM 


Fjg.  201. — Showing  the  movements  of  some  vorticellse  and  the  retraction  of  tlieir 
spiral  stalks.  The  series  must  be  followed  from  left  to  right,  commencing  with 
the  upper  illustrations. 

This  example  is  but  one  of  the  many  interesting  ones 
that  could  have  been  chosen,  and,  moreover,  the  way 
in  which  the  figure  is  reproduced  (namely,  simili- 
gravure),  necessitates,  in  the  case  of  such  small  objects, 
some  alteration  in  the  images.  In  typography,  the 
shaded  parts  have  to  be  indicated   by  cross-hatching, 


MICROSCOPIC  CHROXOPHOTOGRAPHY     299 

which  causes  an  uncertainty  of  outline,  and  an  inter- 
ruption of  continuity. 

Further,  in  the  reproduction  of  microscopical  photo- 
graphs, it  is  always  as  well  to  have  recourse  to  thick 
inks. 

The  Movement  of  the  Blood  in  Capillary  Vessels. — 
The  capillaries  in  the  mesentery  of  a  triton  serve 
excellently  for  this  purpose.  A  layer  of  the  peritoneum 
is  stretched  over  a  piece  of  cork  which  has  a  hole 
bored  through  the  centre,  through  which  the  light 
can  penetrate.  A  fine  capillary  is  manipulated  into 
the  centre  of  the  field  on  the  ground-glass  plate. 
Outside  the  vessel  the  extravasated  red  and  white 
corpuscles  are  motionless,  but  within  the  vessel  they 
are  hurried  along  in  a  rapid  but  somewhat  inter- 
mittent stream.  If  the  different  members  of  a  series 
of  photographs  are  compared,  it  is  quite  obvious  that 
there  is  some  movement  from  the  changes  in  arrange- 
ment which  can  be  noticed  among  the  corpuscles ;  the 
rapidity  of  movement  can  be  actually  estimated  by 
measuring  the  distance  traversed  between  two  successive 
exposures,  namely,  the  distance  traversed  in  ^jj  part 
of  a  second.  For  instance,  if  the  space  traversed 
during  five  separate  exposures  is  about  4  centimetres, 
say  20  centimetres  per  second,  and  the  degree  of 
magnification  is  about  90  diameters,  the  actual  velocity 
will  be  a  little  more  than  2  millimetres  per  second. 

Hence,  what  we  call  the  "circulatory  torrent," 
though  it  appears  very  swift  to  the  eye,  is  in  reality 
a  very  sluggish  stream. 

Movement  of  Zoospores. — In  the  realm  of  vegetable 
Physiology  many  curious  movements  are  to  be  noticed ; 
there  is  one  in  particular  which  we  thought  would  be 
interesting  to  reproduce,  namely,  that  of  the  zoospores 
within  conferva  cells.  These  water-plants  are  com- 
posed   of    filaments    consisting    of    a   series    of  cells 


300  MOVEMENT 

arranged  in  regular  rows,  and  capable  of  ramifying 
in  different  directions.  Some  of  these  cells  at  certain 
times  are  quite  full  of  protoplasm,  and  in  a  photograph 
appear  as  a  dark  mass,  limited  by  a  transparent 
cellulose  membrane. 

Later  on,  the  cells  evacuate  their  contents  more  or 
less  completely ;  they  are  then  seen  to  be  reduced  to 
a  transparent  membrane  which  is  indicated  in  a 
photograph  as  a  clear  outline.  Concerning  this 
phenomenon,  botanists  have  discovered  one  of  the  most 
extraordinary  facts  in  organic  life.  The  protoplasm 
which  at  first  completely  fills  the  cells  as  a  homo- 
geneous amorphous  mass  becomes  aggregated,  and 
breaks  up  into  a  number  of  portions,  each  of  which 
develops  at  one  or  other  extremity  a  pair  of  vibrating 
cilia. 

These  units  take  an  independent  movement,  but  as 
long  as  they  are  encapsuled  within  the  cell  the  move- 
ment is  feeble.  As  soon,  however,  as  part  of  the  cell 
wall  ruptures,  the  small  bodies  escape  through  the 
opening  and  swarm  about  outside  in  the  water  by 
means  of  their  vibrating  cilia.  The  little  bodies  are 
zoospores  ;  it  is  generally  at  sunrise  that  the  escape  is 
effected,  and  the  movements  during  the  first  hours  of 
freedom  are  very  active. 

The  movements  of  the  zoospores  may  be  followed 
throughout  by  observing  in  a  series  of  photographs 
the  successive  positions  they  occupy  in  the  mother 
cell.  But  no  adequate  description  could  be  given 
to  those,  who  have  never  watched  the  phenomenon,  of 
the  activity  which  reigns  within  the  cell,  and  only 
ceases  when  all  the  zoospores  have  succeeded  in 
effecting  their  escape. 

The  Use  of  the  Solar  Microscope  in  Chronophoto- 
graphy. — The  practical  application  of  the  method 
which  has  just  been  described  presents  some  difficulty 


MICROSCOPIC  CHRONOPHOTOGRAPHY  301 

when  it  is  required  to  observe  the  movements  of  certain 
infusoria  as  they  swarm  about  in  the  field  of  the 
microscope.  Hardly  has  the  presence  of  these  creatures 
within  the  field  of  the  microscope  been  assured  before 
they  move  out  of  range  and  necessitate  a  new  adjustment 
of  the  apparatus  ;  for  instance,  they  will  disappear 
during  the  act  of  removing  the  prism  which  projects 
the  image  upon  the  sensitized  film,  or  while  the 
apparatus  is  being  set  in  motion.  Accurate  focussing 
is  difficult  to  effect  because  the  equalization  of  the 
focus  of  the  eye-piece  and  of  the  sensitized  plate  is  a 
delicate  operation. 

These  difficulties  may  be  surmounted  by  the  follow- 
ing contrivance  which  seems  to  us  to  be  applicable  in 
all  cases.  We  locate  ourselves  in  a  dark  room  into 
which  the  sunlight,  reflected  by  a  heliostat,  can  pene- 
trate through  a  hole  in  the  shutter.  The  luminous 
rays  are  made  to  traverse  a  vessel  containing  a  solution 
of  alum,  and  to  converge  on  to  the  preparation  by 
means  of  a  condenser. 

The  image  formed  by  the  microscopic  object-glass 
is  received  upon  a  screen.  A  hole  is  made  in  this 
screen  of  the  same  size  and  shape  as  the  admission 
aperture,  and  behind  this  hole  the  chronophotographic 
apparatus  is  placed. 

The  front  part  of  the  latter  is  removed  and  the 
hinder  part  is  provided  with  circular  diaphragms 
which  rotate  in  front  of  the  admission  aperture.  In 
this  way  the  images  of  moving  creatures  can  be  seen 
crossing  the  screen,  and  the  moment  can  be  seized 
at  which  these  images  appear  at  the  aperture ;  at  this 
moment  it  is  clear  that  they  must  be  within  the 
field  of  the  sensitized  plate  which  is  situated  exactly 
behind. 

The  knob  may  be  pressed,  and  a  series  of  photo- 
graphs taken.  If  the  image  is  noticed  to  leave  the 
21 


302  MOVEMENT 

opening,  and  reappear  upon  the  screen,  the  knob  must 
no  longer  be  pressed,  so  that  the  process  of  taking 
photographs  may  cease.  When  the  creatures  are 
again  noticed  to  be  in  a  favourable  position,  the  opera- 
tion may  be  continued. 

There  are  many  advantages  in  this  method ;  firstly, 
it  enables  the  operator  to  focus  more  accurately,  because 
he  can  directly  gauge  the  definition  of  the  image  at 
the  moment  of  exposure ;  and,  secondly,  it  allows  him 
to  avail  himself  of  fugitive  phenomena  which  would 
otherwise  be  lost,  especially  if  it  is  necessary  to 
make  rather  complicated  arrangements  before  exposing 
the  plate ;  and,  finally,  it  protects  him  from  injurious 
exposure  to  light,  in  case  it  should  fall  upon  the  retina, 
a  danger  which  is  threatened  in  other  methods,  because 
the  light  which  is  thrown  by  the  heliostat,  and  con- 
centrated by  the  condenser,  may  by  chance  traverse 
the  tube  of  the  microscope. 

In  this  way  we  obtained  photographs  of  infusoria  in 
motion,  the  contraction  of  the  internal  organs  of  certain 
larvae,  the  action  of  the  limbs  and  prehensile  appen- 
dages of  all  kinds  of  microscopic  creatures.  There 
even  seems  a  possibility  of  discovering  some  curious 
facts  as  to  muscular  contraction  from  observing  certain 
transparent  larvae. 

This  method  is  also  well  adapted  for  studying  the 
crystallization  of  different  salts.  If  a  saline  solution 
be  concentrated  by  means  of  evaporation,  crystals 
make  their  appearance.  There  is  a  special  form  for 
each  salt,  and  from  these  centres  of  crystallization  a 
variety  of  arborizations  radiate  in  all  directions,  and 
invade  the  microscopic  field  with  unequal  rapidity. 
The  formation  of  these  crystals  can  be  well  seen  on 
the  screen,  and  as  soon  as  the  edge  of  the  crystalline 
development  is  noticed  to  spread  over  the  admission 
aperture  the  photographs  can  be  taken.     Each  image 


MICROSCOPIC  CHRONOPHOTOGRAPHY  303 

shows  a  different  phase  of  development.  The  incom- 
plete attempts  which  we  have  been  able  so  far  to  make 
show  that  microscopic  chronophotography  would  be 
capable  in  more  practised  hands  than  ours  of  producing 
important  results.  In  fact,  we  propose  to  continue  this 
line  of  investigation. 


CHAPTER   XVIII 

SYNTHETIC   RECONSTRUCTION    OF   THE   ELEMENTS 
OF    AN    ANALYZED    MOVEMENT 

Summary.— Plateau's  method;  his  phcnakistoscope  The  zootrope ; 
its  applications  to  the  study  of  horses'  paces  and  their  relations  to 
one  another— The  use  of  instantaneous  photography  in  con- 
nection with  the  zootrope  —  Muybridge,  Anscliutz  —  Scientific 
applications  of  Plateau's  method — Points  of  a  good  apparatus — 
Improvements  made  by  different  authors — Attempts  at  construct- 
ing a  chronophotographic  projector. 

Although  chronophotography  represents  the  suc- 
cessive attitudes  of  a  moving  object,  it  affords  a  very 
different  picture  from  that  which  is  actually  seen  by 
the  eye  when  looking  at  the  object  itself. 

In  each  attitude  the  object  appears  to  be  motionless, 
and  movements,  which  are  successively  executed,  are 
associated  in  a  series  of  images,  as  if  they  were  all 
being  executed  at  the  same  moment. 

The  images,  therefore,  appeal  rather  to  the  imagina- 
tion than  to  the  senses.  They  teach  us,  it  is  true,  to 
observe  Nature  more  carefully,  and,  perhaps,  to  seek 
in  a  moving  animal  for  positions  hitherto  unnoticed. 

This  education  of  the  eye  may,  however,  be  rendered 
still  more  complete  if  the  impression  of  the  movement 
be  conveyed  to  the  eye  under  conditions  to  which  it  is 
accustomed.  Such  is  the  object  of  Stroboscopy,  a 
method  of  immense  scientific  importance.  The  princi- 
ples of  this  method  were  discovered  by   Plateau,  and 


SYNTHESIS   OF   MOVEMENT  305 

they  depend  on  the  physiological  property  of  the  retina 
of  retaining  for  a  brief  moment  the  impression  of  an 
image  after  the  object  which  has  produced  it  has 
disappeared.  The  duration  of  this  retinal  picture  is 
estimated  at  -^  part  of  a  second.  So  that  if  an  image 
is  placed  before  our  eyes  ten  times  in  a  second  the  idea 
of  discontinuity  is  lost,  and  the  images  appear  to 
be  in  continual  evidence. 

If  the  images  shown  to  us  are  represented  in  the 
successive  positions  assumed  by  the  object  in  motion, 
the  impression  conveyed  to  the  eye  is  that  of  a  con- 
tinuous movement  with  no  intermission.  Now,  we  have 
seen  that  not  only  10,  but  even  20,  40,  or  60  images 
can  be  produced  by  chronophotography  per  second. 
If  the  60  photographs  taken  during  one  step  of  a 
galloping  horse  could  be  passed  before  the  eyes  at  the 
rate  of  10  per  second,  the  duration  of  the  whole  step 
would  be  spread  over  a  period  of  6  seconds,  and  hence 
we  should  have  a  considerable  time  in  which  to  observe 
the  motion  of  the  limbs,  so  hard  to  follow  under  normal 
conditions. 

In  the  same  way  a  flying  bird  could  be  represented 
with  slower  wing  movement,  and  so  too  with  other 
phenomena  which  escape  notice  on  account  of  their 
extreme  rapidity. 

Inversely,  when  a  movement  is  so  slow  as  to  escape 
observation,  photographs  could  be  taken  of  it  at  long 
intervals  and  presented  to  the  eyes  in  sufficiently  rapid 
succession  to  allow  of  the  changes  being  clearly  per- 
ceptible. In  other  cases,  if  the  photographs  are  pre- 
sented to  the  eye  at  the  same  intervals  as  separate 
the  successive  exposures,  the  movement  will  appear  as 
it  actually  took  place.  Such  is  the  use  of  the  strobo- 
scope. We  will  now  show  the  successive  developments 
of  this  method. 

Plateau's    Phenakistoscope.  —  Everybody  knows  the 


306  MOVEMENT 

ingenious  toy  invented  by  Plateau  at  the  beginning  of 
the  present  century,  and  to  which  he  gave  the  name  of 
"  Phenakistoscope." 

The  original  form  of  this  instrument  was  a  play- 
thing which  delighted  us  as  children;  it  was  destined, 


Fig.  202— Disc  of  a  phenakistoscope,  showing  the  different  phases  of  movement  of  a 
gull's  wing. 

however,  one  day,  to  be  used  for  more  interesting 
purposes.  The  phenakistoscope  consists  of  the  follow- 
ing parts,  a  cardboard  disc  perforated  at  equal  distances 
round  the  periphery  by  small  slits.  One  side  of  the 
disc  is  blackened,  and  on  the  other  a  series  of  images 


SYNTHESIS  OF  MOVEMENT  307 

are  arranged  representing  men  or  animals  in  the  various 
attitudes  which  correspond  to  the  successive  phases  of 
a  movement. 

When  the  disc  is  spun  round  on  its  axis  opposite  to 
a  mirror,  and  the  eye  applied  to  the  blackened  side  on 
a  level  with  the  revolving  slits,  the  reflections  of  the 
various  images  are  seen  one  after  another  corresponding 
to  the  different  attitudes  assumed  by  the  original 
object;  this  conveys  an  impression  of  actual  movement. 
Fig.  202  represents  the  disc  of  a  phenakistoscope ;  on 
it  are  arranged  the  successive  photographs  of  a  flying 
gull. 

If  this  side  is  made  to  revolve  in  front  of  a  mirror 
and  the  eye  be  applied  on  a  level  with  the  slits,  the 
gull  can  be  seen  flapping  its  wings.  The  rapidity  of 
the  movement  depends  on  the  velocity  of  rotation. 

The  disc  must  be  turned  in  the  right  direction,  other- 
wise the  images  will  succeed  one  another  in  the  inverse 
order  to  that  in  which  they  actually  occur,  and  the 
direction  of  movement  will  appear  reversed. 

Zootropes. — The  manufacture  of  these  articles  became 
a  commercial  industry,  and  some  of  them  were  turned  out 
in  more  convenient  forms  ;  one  of  them  was  called  the 
"zootrope,"  and  consisted  of  a  cylindrical  chamber 
revolving  on  a  vertical  axis.  Narrow  upright  slits 
were  made  round  the  brim,  and  inside  the  cylindrical 
wall  a  strip  of  paper  was  pasted  on  which  a  series  of 
images  was  arranged  so  as  to  represent  the  successive 
attitudes  of  a  man  or  animal  in  motion.  If  these 
figures  were  observed  through  the  slits  while  the 
zootrope  was  revolving,  the  same  impression  as  that 
caused  by  the  phenakistoscope  was  produced. 

This  contrivance,  which  has  been  adopted  by  many 
manufacturers, possesses  one  obvious  advantage, namely, 
that  several  people  arranged  round  the  apparatus  can 
watch  the  phenomenon  at  the  same  time. 


308  MOVEMENT 

Application  of  the  Zootrope  to  the  Study  of  Horses' 
Paces. — In  the  year  1867  we  made  use  of  the  zootrope 
for  the  purpose  of  representing  the  various  paces  of  a 
horse  in  motion,  and  also  for  showing  how  the  various 
paces  differed  from  one  another.  The  latter  could  be 
shown  by  merely  altering  the  sequence  of  the  move- 
ments of  the  fore  and  hind  limbs.  This  was  the 
concrete  demonstration  of  the  sequence  expressed  by 
the  chronographic  charts. 

At  this  time  instantaneous  photography  had  not 
been  thought  of,  and  so  we  used  simple  drawings  to 
show  the  successive  positions,  our  data  were  derived 
from  the  registered  charts  and  from  the  actual  foot- 
tracks. 

We  chose  first  the  simplest  case,  namely,  the  paces 
of  an  ambling  horse,  in  which  the  two  limbs  on  the 
same  side  acted  simultaneously.  Twelve  positions  were 
drawn  on  a  long  strip  of  paper,  six  to  represent  the 
rise  of  the  two  feet  on  the  right-hand  side,  the  other  six 
to  represent  their  period  of  contact  on  the  ground,  the 
two  feet  on  the  left-hand  side  were  of  course  in  the 
opposite  phases. 

By  arranging  this  strip  of  paper  in  tne  zootrope,  the 
paces  of  an  ambling  horse  could  be  easily  recognized 
through  the  slits. 

Now,  for  the  purpose  of  showing  how  the  other  paces 
could  be  derived  from  those  of  ambling,  we  had  recourse 
to  the  following  device.  Vertical  lines  were  drawn 
through  the  middle  of  the  horses'  bodies,  and  square 
frames  were  constructed  round  the  posterior  halves  of 
the  figures  containing  the  hind  limbs  of  the  animals. 
The  squares  of  paper  were  then  cut  out,  and  the 
original  strip  of  paper  then  remained,  representing  a 
series  of  positions  of  the  fore  quarters,  and  behind 
each  of  these  mutilated  images  there  appeared  a  square 
hole  in  the  paper.     The  strip  of  paper  was  then  placed 


SYNTHESIS   OF   MOVEMENT  309 

on  another  of  the  same  size,  and  the  hind  portions  of 
the  images  which  had  been  cut  away  were  gummed 
each  in  its  proper  position  upon  the  lower  strip.  When 
this  was  done,  the  two  strips  taken  together  presented 
the  appearance  of  the  original  slip,  namely,  the  suc- 
cessive attitudes  of  an  ambling  horse  during  the 
performance  of  one  stride.  If  the  lower  strip  is  moved 
on  one  place,  so  that  the  fore  feet  of  one  image  are 
united  to  the  hind  feet  of  the  image  immediately 
behind  it,  the  fore  feet  will  be  T\r  of  a  step  in  advance 
of  the  hind  feet,  and  the  whole  series  thus  broken  up 
will  give  the  appearance  in  the  zootrope  of  a  racking 
pace,  in  which  the  hind  limbs  slightly  anticipate  the 
movements  of  the  fore  limbs. 

By  sliding  the  lower  strip  of  paper  a  little  further 
forward  the  appearance  of  a  walking  pace  is  produced. 
Still  another  move  in  the  same  direction  and  we  have 
a  broken  trot,  and  then  again  a  walk. 

This  is  the  concrete  expression  of  the  relations  given 
by  the  chronographic  chart  Fig.  123. 

With  this  method  persons  familiar  with  horses'  paces 
can  recognize  each  example,  and  realize  its  derivation 
from  the  others.  We  have  been  most  ably  seconded 
in  these  researches  by  M.  Mathias  Duval,  now  professor 
at  the  Faculty  of  Medicine  and  at  the  School  of  Fine 
Arts.  This  savant  recognized  the  importance  of  this 
method  for  teaching  complicated  and  rapid  movements 
such  as  could  otherwise  only  be  learned  at  the  cost  of 
much  labour  by  specialists.  M.  Zecky,  professor  at  the 
School  of  Fine  Arts  at  Vienna,  has  adopted  the  same 
method  for  representing  horses'  paces.  We  still  possess 
some  very  carefully  drawn  series  which  he  sent  us. 

Use  of  Instantaneous  Photography  in  connection  with 
the  Zootrope. — In  this  method  the  accuracy  with  which 
the  paces  were  represented  was  entirely  dependent 
on  the  skill  of  the  artist,  and  hence  it  was  left  for 


310  MOVEMENT 

photography  to  perfect  the  zootropic  representation 
of  motion. 

From  the  time  when  Mr.  Muy bridge  succeeded  in 
taking  a  photographic  series  of  the  positions  assumed 
by  men  and  animals  in  motion,  he  invariably  resorted 
to  Plateau's  method  for  synthesizing  the  movements 
he  had  analyzed. 

The  apparatus  used  by  Mr.  Muybridge  was  a  sort  of 
projection  phenakistoscope,  in  which  pictures  of  horses 
painted  on  glass  discs,  and  copied  from  the  author's 
photographs,  were  placed  in  the  focus  of  the  projecting 
lantern  and  made  to  rotate.  Slits  made  in  the  discs 
admitted  light  at  the  required  moments.  A  consider- 
able audience  could  thus  see  upon  the  screen  sil- 
houettes of  horses  moving  in  various  directions  and  at 
various  paces. , 

Zootropes  of  Muybridge  and  Anschiitz. — We  have 
already  remarked  that  the  figures  were  painted.  Now, 
one  great  disadvantage  of  Muybridge's  apparatus,  and, 
indeed,  of  the  zootrope  itself,  is  that  the  figures  are 
out  of  proportion,  owing  to  their  reduction  in  the 
transverse  direction,  so  that  the  painted  horses  on  the 
revolving  discs  have  to  be  made  longer  than  they 
really  are,  so  as  to  appear  in  their  true  proportions 
when  thrown  upon  the  screen. 

M.  Anschiitz  prepared  for  the  ordinary  zootrope 
strips  of  paper  covered  with  photographic  prints  of 
men  and  animals  in  motion.  In  this  case  the  figures 
were  distorted ;  horses  especially  showed  an  appreciable 
diminution  in  length. 

Solid  Figures  in  the  Zootrope. — We  also  made  use  of 
the  zootrope  in  studying  the  movements  of  birds' 
wings,  and  for  this  purpose  we  resorted  to  a  particular 
contrivance.  Instead  of  a  strip  of  paper  covered  with 
figures,  we  introduced  into  the  zootrope  a  series  of 
wax  models  painted  in  oils,  and  representing  the  bird 


SYNTHESIS   OF  MOVEMENT 


311 


in  all  the  successive  phases  of  its  wing  increment. 
The  illusion  was  complete,  and  a  flying  bird  could  be 
seen  flying  round  and  round  the  apparatus ;  sometimes 
flying  away  from  the  observer,  sometimes  across,  and 
sometimes  towards  him.* 

Scientific  Applications  of  Plateau's  Method. — All  these' 
applications  would   be   simply   childish   if  they  were 


Fig.  2U3.— Zoutrope,  with  figures  of  a  gull  in  relief,  and  in  the  successive  attitudes 
of  flight. 


limited  to  the  reproduction  of  phenomena  which  could 
be  observed  by  the  eye  in  the  case  of  living  creatures. 
They  would  be  attended,  in  fact,  by  all  the  uncertainties 
and  difficulties  which  embarrass  the  observation  of  the 
actual  movement.  In  a  bird,  for  instance,  the  wings 
could  only  be  distinguished  as  an  indistinct  mass,  just 

*  This  zootrope  with  solid  figures  is  still  preserved  at  the  Physio- 
logical Station. 


312  MOVEMENT 

as  they  appear  in  nature.  Bat  a  combination  of  the 
zootrope  and  chronophotography  has  further  possibili- 
ties, for  it  enables  the  observer  to  follow  movements, 
which  would  otherwise  be  impossible  to  examine,  by 
slowing  down  the  motion  to  any  desired  rate.  We 
have  already  pointed  out  during  a  single  stroke  of  the 
wing,  which  lasts  J  of  a  second,  a  series  of  twelve 
photographs  can  be  taken  at  intervals  of  c}6  of  a  second. 
Now,  these  twelve  photographs,  which  correspond  to  a 
single  stroke  of  the  wing,  can  be  made  to  pass  before 
the  eye  in  one  second.  This  succession  is  sufficiently 
rapid  to  produce  an  impression  of  continuous  motion. 
Under  these  conditions,  the  rate  of  movement  is  reduced 
to  one-fifth  of  its  actual  velocity,  and  the  eye  can  follow 
it  in  all  its  phases,  whereas,  in  a  living  bird,  only  a 
confused  flutter  of  the  wings  can  be  distinguished. 

In  the  same  way,  by  slowing  down  the  phases  of  a 
horse's  paces  by  means  of  the  zootrope,  they  can  be 
more  easily  analyzed  than  by  observations  made  directly 
on  the  animal. 

It  is  not,  however,  only  by  reason  of  their  rapidity 
that  some  movements  elude  observation,  sometimes 
their  very  slowness  renders  them  inaccessible  to  our 
senses,  take,  for  instance,  the  growth  of  animals  and 
plants.  These  movements  may,  however,  become  quite 
visible  if  they  are  photographed  at  considerable  inter- 
vals of  time,  and  the  corresponding  series  of  images 
passed  rapidly  before  the  eyes  by  means  of  the 
zootrope. 

Professor  Mach,  of  Vienna,  suggests  a  curious  line 
of  research  by  means  of  this  method.  His  idea  is  to 
take  a  number  of  photographs  of  an  individual  at  equal 
intervals  of  time,  from  earliest  infancy  until  extreme 
old  age,  and  then  to  arrange  the  series  of  images  thus 
obtained  in  Plateau's  phenakistoscope.  If  this  were 
done,  a  series  of  changes,  which  had  been  brought 


SYNTHESIS   OF   MOVEMENT  313 

about  during  a  period  of  many  years,  would  pass  before 
the  eyes  of  the  beholder  in  the  course  of  a  few  seconds, 
and  thus  the  stages  of  a  man's  existence  would  pass 
in  review  before  the  gaze  of  the  onlookers  in  the  form 
of  a  strange  and  marvellous  metamorphosis. 

This  method  invented  by  Plateau  seems  likely  to 
extend  our  knowledge  as  regards  all  kinds  of  pheno- 
mena. But  the  future  of  the  method  is  dependent  on 
the  possible  correction  which  can  be  effected  in  the 
distortion  of  the  images,  and  on  the  discovery  of  a 
satisfactory  means  of  projecting  a  number  of  moving 
figures  on  a  screen,  so  as  to  be  visible  to  a  large 
audience.  And,  further,  it  will  be  necessary  to  augment 
the  number  of  successive  photographs,  so  as  to  represent 
a  performance  of  considerable  duration. 

Improvements  suggested  by  Different  Makers. — 80 
that  the  images  might  be  projected  without  distortion, 
several  object-glasses  were  arranged  in  a  circle,  and 
at  the  focus  of  each  positive  images  were  arranged 
representing  the  different  phases  of  a  movement,  All 
the  object-glasses  were  directed  towards  the  same 
spot  on  the  screen  in  such  a  way  that  by  successively 
illuminating  each  of  the  positive  images  placed  behind 
them,  the  corresponding  attitudes  were  successively 
projected  on  the  screen.  To  effect  the  successive 
illuminations  of  the  slides,  it  has  been  suggested  that 
a  Drumont  lamp  should  be  made  to  revolve  as  a  source 
of  light. 

Images  projected  in  this  way  ought  to  be  perfect ; 
but  the  focussing  of  each,  and  the  determination  of 
the  direction  of  the  object-glasses,  would  be  a  most 
laborious  operation.  Moreover,  the  number  of  object- 
glasses  is  necessarily  limited  to  five  or  six,  and  thus 
the  extent  of  the  movement  periodically  repeated, 
as  the  lamp  completes  its  revolution,  is  necessarily 
very  short. 


314  MOVEMENT 

M.  Raynaud's  Praxinoscope. — Under  this  title,  M. 
Raynaud  has  given  to  the  world  an  extremely  ingenious 
instrument.  As  in  the  ordinary  zootrope,  the  figures 
are  arranged  within  a  cylinder,  and  are  reflected  by  a 
prismatic  mirror  situated  at  the  centre  of  the  apparatus, 
and  thence  reach  the  eye  of  the  observer.  The  con- 
trivance is  peculiar  in  that  the  substitution  of  one 
position  for  another  is  effected  without  any  intermediate 
eclipse,  so  that  the  images,  owing  to  the  constant 
illumination,  appear  exceedingly  bright.  By  inter- 
posing a  photographic  object-glass  in  the  path  of  the 
reflected  images,  M.  Raynaud  has  thrown  them  upon 
a  screen,  and  magnified  them  to  the  required  dimensions. 
Finally,  by  substituting  for  the  flat  circular  strip  of 
figures  a  long  strip  which  winds  off  one  roller  on  to 
another,  the  writer  has  been  able  to  display  a  per- 
formance of  considerable  duration.  As  yet,  M.  Raynaud 
has  only  employed  figures  drawn  or  painted  by  hand ; 
doubtless  he  could  obtain  remarkable  results  by 
substituting  a  series  of  chronophotographs.  A  slight 
defect  in  the  apparatus  is  that  the  plane  of  the  pro- 
jected images  is  slightly  oblique  as  regards  the  principal 
axis  of  the  object-glass,  this  is  due  to  the  construction 
of  the  apparatus.  It  is  thus  impossible  that  all  the 
parts  of  the  images  can  be  in  focus,  and  hence  the 
projection  on  the  screen  is  somewhat  indistinct. 

M.  Demeny's  Ph otophone. — M.  Demeny  has  employed 
another  method  for  reproducing  the  movements  of  the 
face,  the  tongue,  and  the  lips,  executed  during  speech. 
My  assistant  at  the  Physiological  Station  has  prepared 
on  a  length  of  film  a  chronophotographic  series  con- 
sisting of  twenty-four  portraits  of  a  man  articulating 
certain  words.  When  this  series  of  portraits  was  trans- 
ferred to  the  circumference  of  a  glass  disc  and  placed 
in  the  focus  of  a  photographic  object-glass,  they  were 
brightly  illuminated  from  behind,  and  rendered  visible 


SYNTHESIS   OF   MOVEMENT  315 

for  brief  intervals  by  an  arrangement  of  fenestrated 
diaphragms,  as  used  in  ehronophotography.  The  short- 
ness of  the  exposures,  and  the  perfect  working  of  this 
apparatus,  represented  the  images  as  immovable,  and 


Fig   204. — Derueny's  photophone. 

fhey  appeared  exactly  at  the  same  spot,  in  spite  of  the 
rotation  of  the  disc  upon  which  they  were  placed.* 

These  photographs  give  such  a  perfect  representation 
of  speech  that  deaf  mutes  accustomed  to  read  the 
movements  of  the  lips  have  been  able  to  recognize 
the  words  spoken  by  the  person  photographed. 

*  This  instrument  was  designed  by  M.  Demeny,  and  called  the 
"Photophone  "  (C.  R.  de  VAcademie  des  Sciences,  July  27,  1891). 


316  MOVEMENT 

I  doubt  whether  it  is  possible  to  make  a  more 
perfect  zootrope,  and  yet  there  are  a  few  defects  that 
one  can  mention.  Firstly/  the  number  of  images  that 
can  be  transferred  to  the  disc  is  necessarily  limited, 
unless  the  apparatus  is  of  enormous  size  ;  and,  secondly, 
since  a  good  definition  of  the  movements  can  only  be 
obtained  by  very  brief  exposure,  it  follows  that  the 
amount  of  light  given  off  must  be  too  small  to  produce 
with  distinctness  an  enlarged  projection,  and  this  is 
the  case  even  when  the  source  of  illumination  is  of 
the  most  powerful  description. 

This  list  of  the  different  forms  of  apparatuses  used 
in  the  synthesis  of  movement  is,  no  doubt,  incomplete  ; 
but  it  may  serve  to  indicate  the  respective  advantages 
and  disadvantages  of  each  system,  and  to  serve  as  a 
guide  to  those  who  may  wish  to  make  fresh  researches 
in  the  same  direction. 

The  Points  of  a  Good  Apparatus. — In  apparatuses  in 
which  the  figures  rotate  with  a  continuous  movement 
the  image  can  only  be  made  to  appear  motionless  by 
giving  such  a  short  exposure  that  the  movement 
during  that  time  is  inappreciable. 

Now,  the  brevity  of  the  period  of  illumination 
entails  a  considerable  loss  of  light,  and  hence  the 
image,  when  projected  on  a  large  scale,  is  hardly 
visible  at  all.  If,  on  the  other  hand,  it  is  necessary 
to  produce  a  brilliant  projection,  the  duration  of  the 
exposure  must  be  as  long  as  possible ;  in  that  case, 
however,  the  image  which  is  for  the  time  being  under 
observation  must  be  absolutely  motionless.  It  is 
obviously  impossible  to  ensure  alternate  periods  of 
rest  and  motion  with  discs  or  other  heavy  pieces 
of  revolving  apparatus.  The  solution  of  this  pro- 
blem is  the  same  as  that  which  we  adopted  in 
chronophotogiapliy.  The  apparatus  which  is  used 
for  the  analysis  of  movement  is  reversible,  at  least  in 


SYNTHESIS   OF  MOVEMENT  317 

principle,  and  might  be  used  for  their  synthetic  re- 
construction. Let  us  imagine  that  a  strip  of  film  has 
imprinted  on  it  positive  images,  and  that  this  strip 
is  placed  at  the  focus  of  the  object-glass,  and  brightly 
illuminated  from  behind.  If  these  figures  are  then 
projected  on  a  screen  as  far  removed  from  the  object- 
glass  as  were  the  original  objects,  the  figures  will 
appear  to  actual  scale. 

Every  time  the  objective  is  exposed  by  the  rotation 
of  the  diaphragm  an  image  is  thrown  on  the  screen, 
the  outlines  of  which  are  perfectly  defined,  because 
the  film  is  arrested  by  compression  at  the  moment 
of  exposure.  As  a  matter  of  fact,  it  is  better  to  adopt 
a  special  contrivance  for  projecting  moving  figures. 

The  following  are  the  reasons  which  induced  us  to 
construct  a  new  instrument,  to  which  we  have  given 
the  name,  "  Chronophotographic  projector." 

The  Chronophotographic  Projector. — In  a  projecting 
apparatus  the  exposure  should  be  as  long  as  possible, 
and  the  transparency  should  be  arrested  during  the 
whole  period  of  its  projection  upon  the  screen.  These 
conditions  must  be  fulfilled  if  bright  and  clear  images 
are  required.  In  the  case  of  the  analyzing  apparatus, 
the  exposures,  on  the  contrary,  should  be  as  brief  as 
the  illumination  will  allow.  For  an  insect's  wins:, 
the  exposure  should  be  no  more  than  25000  Part 
of  a  second.  Xow,  with  such  a  short  exposure,  an 
image  would  be  almost  invisible  if  greatly  enlarged  by 
projection ;  and  this  would  still  be  the  case  even 
were  the  source  of  illumination  very  powerful.  The 
most  important  point  in  constructing  a  projector  is 
to  secure  as  long  an  exposure  as  is  possible.  For 
instance,  if  ten  images  were  taken  per  second,  the 
exposure  should  be  half  or  a  third  as  long ;  that  is 
to  say,  for  ^0  or  30  °f  a  second,  instead  of  for  j-^qq  of 
a  second,  which  is  the  usual  exposure  allowed  by 
22 


318  MOVEMENT 

an  analyzing  apparatus.  Instead  of  the  small  fenestra- 
tions on  the  circular  diaphragms,  long  slits  should  be 
made,  occupying  a  third  of  their  circumference. 
During  this  long  exposure,  the  film  should  be  com- 
pletely arrested,  and  for  this  purpose  the  compressor 
should  have  a  particular  kind  of  cam. 

To  realize  the  nature  of  a  movement  satisfactorily, 
it  is  as  well  to  reproduce  it  several  times.  This  may 
easily  be  done  by  an  apparatus  fitted  with  revolving 
discs ;  but,  as  in  our  apparatus,  we  have  to  use  a  length 
of  film,  it  should  be  glued  together  at  the  ends, 
so  as  to  produce  an  endless  series  of  images  continually 
rotating  at  the  focus  of  the  objective.  Such  a  strip  as 
this  could  not  be  introduced  into  the  ordinary  chrono- 
photographic  apparatus. 

We  have  therefore  constructed  a  special  apparatus, 
in  which  an  endless  length  of  film  containing  forty  or 
sixty  figures,  or  even  more,  is  allowed  to  pass  with- 
out cessation  under  the  field  of  the  objective. 

The  illumination,  which  is  from  behind,  and  consists 
either  of  the  electric  light  or  the  sun  itself,  projects 
these  figures  upon  a  screen.  This  instrument  produces 
very  bright  images,  but  it  is  noisy,  and  the  projected 
figures  do  not  appear  as  absolutely  motionless  as  one 
could  wish. 

Having  arrived  at  this  point  in  our  researches,  we 
learned  that  our  mechanic  had  discovered  an  im- 
mediate solution  of  this  problem,  and  by  quite  a 
different  method ;  we  shall  therefore  desist  from 
our  present  account  pending  further  investigations. 


INDEX 


Advancing  wave,  appearance  of,  93 
Aerial  locomotion,  226-257 
Apparatus  for  chronophotography 

on  moving  plates,  110-112 
for  microscopic  chronoplioto- 
graphy, 295 

for  o  iography,  43-47 

Arachnids,  locomotion  of,  270 
Arts  and  crafts,  academy  of,  24 
Assyrian  bas-relief,  204 
Astronomical  revolver,  103,  104 
Avanzini's  theory,  96 


B 


I-allistics,  laws  of,  86 
Bas-relief,  Assyrian,  204 

of  Medynet-Abou,  201 

Batrachians,  locomotion  of,  266 

Beetle,  locomotion  of,  271 

Blood,  movements  of  in  capillaries. 

2H9 
Bobbins  for  sensitized  film,  1 1 7 
Bodies  falling  in  air,  84,  85 
Bodies  of  pisciform  shape,  resist- 
ance of,  97 
Borelli,  126 
Borelli's  law,  226 
Boussinesq,  94 
Box    for     holding    chronographic 

plates,  113 
Boxer,  positions  of,  59 
Bridges,  vibrations  of,  101,  102 


Cardiac  movements,  chronoplioto- 
graphy of,  282-287 

,  graphic  method  of,  276 

Carlet,  134 

Centres  of  movement  in  joints,  289 

Characteristic  attitudes,  177 

Chart  of  fixed  odograph,  131 

of  footprints.  191 

Charts,  chronogra  pi  lie.  8.  11,  12,  13, 
35,  37,  39,  44,  47,  131,  132,  158, 
188,  190 

,   chronophotographic,   52,  55, 

79.  86,  87,  99,  140,  142,  143,  144, 
154,  155,  157 

of  horses'  paces,  189 

,  transition  from  trotting 

to  galloping,  189 

, walking,  189 

,  transition  from  galloping 

to  trotting,  190 

, walking  to  trotting, 

189 

Chevreul,  71 

Chopping  waves,  93 

Chronographic  charts.    See  Charts. 

Chronography,  3 

Chronometric  dial,  15-17,  51 

Chronopliotograph  of  elephant  walk- 
ing, 261 

of  flying  pigeon,  233 

of  horse's  leg  in  walking.  260 

of  jump  with  flexed  leg,  142 

■ with  stiffened  leg,  143 

of  long  jump,  I3.1-l:-i7,  140 

of  man's  leg  in  walking,  260 


320 


INDEX 


Chronophotograph  of  oscillations  of 

leg,  144 

of  pole-jump,  137-139 

of  runner.  173 

of  b word-thrust,  178 

of  walking,  172 

Chronophotographic        apparatus, 

67-83 

,  arrangement  of,  116 

,  charging  of,  118 

camera,  68 

charts.     Si-e  Charts. 

enlargement,  123 

focussing  frame,  69 

objective.  69 

projection,  317 

Chronopliotographs,      enlargement 

of,  123 

,  number  of  images,  123 

,  reduction  of,  I'l'd 

,  reproduction  of,  123 

,  shape  of,  121 

,  size  of,  121 

taken  from  above,  175 

Chronophotography      applied       to 

hydrodynamics,  90 

kinetics,  126 

mechanics,  84 

,  geometrical,  60 

in  sculpture,  176 

,  microscopic,  291-303 

of  avine  flight,  227-230 

of  facial  expression,  180 

on  fixed  plates,  .">4-06 

on  moving  films,  23+ 

plates,  103-125 


Comatula,  locomotion  of, 

Comparative  locomotion, 

among  birds,  261 

terrestrial 

259 

Cones,  23-27 

Conoids.  27 

Cros  and  Carpentier,  14 

Curnieu,  1!»3 

Currents,  95-99 

Curves  of  falling  bodies 

of  odograph,  131 

of  vertical  oscillations  of  head. 

158 

of  work  in  walking  and  run- 
ning, 164,  165 

Cylinders,  23-29 


214 

258-274 

mammals, 


52 


D 


Dark  background,  74 

for  chronophotographv, 

70 

slide,  70 

Demeny,  57,  77.  133,  168 
Deslandres,  101 
Drapery,  183 
Drone,  flight  of,  240 
Duck,  fl  ght  of,  231 
Duval,  Mathias,  309 
Dynamograph,  traction,  157 
Dynamographic  platform,  148 

tracings,  152 

Dynamogr.iphy    and    chronophoto- 
graphy, 153 

Dvnamometer,  149 


Eddies,  95-98 

Eel,  locomotion  of,  217,  268,  269 

Elastic  thread  method,  i2,  150 

Elephant,  locomotion  of,  261 

Engrand,  177 

Emmanuel,  Maurice,  184 

Expressive  attitudes,  179 


Fencing,  photograph  of,  141 
Film,  arrest  of,  at  moment  of  ex- 
posure, 120 
Fish,  locomotion  of,  268 
Flexible  rod,  vibrations  in,  101 
Flight  of  bee,  254,  267 

of  drone,  240 

of  duck,  231 

of  heron,  233 

of  insects,  238-257 

of  pigeon,  from  above,  234 

of  tipulse,  251-256 

Fluid  waves,  (.»1 

Flying  apparatus,  trajectory  of,  89 

Focussing,  82 

Frog,  locomotion  of,  266 


Galileo.  127 

Gecko,  locomotion  of,  265 


INDEX 


321 


Geometrical  chronophotography,  60 

of  high-jump,  155 

of  horse,  20J 

of  leg  movement,  154 

of  man  walking,  157 

Goiffon,  3 


H 


Harvey,  '291 
Heron,  flight  of,  233 
Heuzey,  183 
Hydrodynamics,  90 
Hyperboloids.  23-29 


Locomotion  of  insects,  270-274 

of  lizard,  265 

of  medusa,  216 

of  scorpion,  273 

of  s»  a-horse,  223 

of  shrimp,  225 

of  skate,  2 1 8 

of  snakes,  268 

of  star-fish.  223 

of  tortoise.  264 

,  tvpes  of,  226-257 

Loi  de.  114 
Long-jump,  135 


31 


Images,  alternating,  62 

,  multiplication  of  numher,  62 

,  separation  of.  63 

Influence  of  rate  of  movement,  5S 
Insect  flight,  238-257 

l'icnniotiun,  2i0 

Instantaneous  photograph  of  runner, 
171 


Jansen.  103 
Joints,  289 


Land-snakes,  locomotion  of,  267 
Lever  drums,  5 
Lippmann's  electrometer.  49 
Lizard,  locomotion  of,  265 
Locomotion,  classification  of.  262 

.  comparative.  258-274 

, ,  in  quadrupeds,  186-210 

from    artistic   point  of  view, 

169 

in  water,  211-225 

of  batrachians,  266 

—  of  comatula.  214 

of  eels,  216,  268,  269 

of  fish,  268-275 

of  fly,  252 

of  gecko,  265 


Machinery  hall,  85 

Macrobiosis,  242 

Mechanical  work  in  walking,  155 

Medusa,  locomotion  of,  2 1 5 

Melograph,  14 

Moth'  d  of  recording  muscular  con- 
traction, 228 

Metre  Bcale,  80 

Millet,  46 

Molecular  movements  in  waves, 
33-53 

Movement  from  point  of  view  of 
dynamics,  146 

,   graphic  representation  of,  35 

Movements,  human.  126-145 

in  liquids.  75-77 

in  vorticella,  289 

of  zoospores,  299 

Moving  bodies,  trajectories  of, 
19-:-J2 

Muscular  expression,  174 

work  in  walking,  158,  159 

Muy  bridge,  106,  196 

Muybridge's  zootiope,  310    . 


N 


Naehet,  295,  297 


O 

Ocydromes,  170 
Odography,  43 
Onimus  and  Martin,  59 


322 


INDEX 


Orthopterous  insects,  locomotion  of, 

271 
Oscillations,  99 


Paces  in  man,  128 

,  speed  of,  128 

,  transition  of,  187 

Pages,  208 
Pail  lard,  Gabriel,  10 
Paradoxical  illumination,  30 
Path  described   by  points   on    the 

body,  133 
Pel.ier,  10 

Pendulum,  jointed,  99 
Perspective  of  moving  animals,  81 
Pettigrew's  theory,  243 
Phenakistoscope,  305 
Photographic  gun,  108-113 
trajectory  of  insect  movement, 

248 
Photographs,  directions  for  taking, 

82 
Photography,    influence    on     Art, 

169-180 
Photophone  of  Demeny,  314 
Physiological  Station,  71 
Pianist,  fingering  of,  12 
Pigeon,  flight  of,  234 
Planet  Venus,  transit  of,  104 
Plateau's  phenakistoscope,  305 
Playfair,  2 
Pole-jumping,  137 
Poncelet  and  Morin,  40 
Praxinoscope  of  Raynaud,  314 
Pressure  curves,  152 
Princes  Park,  71 
Pulse,  tracing  of,  41 


Q 

Quadrupeds,  locomotion  of,  186-210 


B 


Record   of  movement   in  walking, 

133 

■ ,  myographic,  229 

Relative  amount  of  work  in  different 

paces,  162 
Running,  chron* 'photography  of,  58 


Sea-horse,  locomotion  of,  222 

Sebert,  locomotion  of,  273 

Shoes,  chronographic,  7 

Shrimp,  locomotion  of,  225 

Simultaneous  photograp  y,  236 

Skate,  locomotion  of,  2 18 

Snakes,  locomotion  of,  268 

Sorhonne,  the,  13 

Space,  measurement  of,  1-32 

Stanford,  105     ' 

Star- fish,  locomotion  of,  223 

Station,  Physiological,  71 

Stereoscopic  pictures,  28,  29 

Stroboscopy,  304 

Synchronism    of   wing    movement, 

241 
Synthesis  of  movement,  304-318 
and  chronophotography,  304- 

318 


Tadpoles,  locomotion  of,  266 
Tatin,  12 
Time,  1-17 

curve,  14 

,  graphic  record  of,  1 

Tipulse,  flight  of,  254-256 
Toads,  locomotion  of,  266 
Tortoise,  locomotion  of,  264 
Train,  chart  of,  36-38 
Trajectories,  stereoscopic,  22 
Trajectory  of  bird's  humerus,  229 

of  insect's  wing,  243 

Trochoids,  92 


Uchard,  88 
Useful  effect.  161 


Vertical  foot-pressure,  laws  of,  150 
oscillations  of  head  in  walk- 
ing, 10? 


Vibrations,  99 
Vincent,  3 


INDEX  323 

Vincent  and  Goiffon,  193  I   Weber  brothers,  127,  131,  156 

Vulscian  bas-relief,  2U4  |    Wellmann,  106 

Vorticella,  movement  of,  298 

z 

W  ! 

!  Zecky,  309 

Walking,  abnorma'ities,  77  i  Zootropes,  307,  310 

Waves,  photographs  of,  y2-95,  121     i  Zoospores,  movement  of,  299 


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f^LTR  JUVENILE  OFFENDERS.    By W.  D.  Mor- 

^S      R1SON. 

RIME  A   SOCIAL    STUDY.     By  Professor  Joly. 


C 


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HE  STORY  OF  THE  EARTH.  By  H.  G.  Sef- 
ley,  F.  R.  S.,  Professor  of  Geography  in  King's  College,  London. 
With  Illustrations. 

HE  STORY  OF  THE  SOIAR  SYSTEM.  By 
G.  F.  Chambers,  F.  R.  A.  S. 


T 
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CLIMBING  IN  THE  HIMALAYAS.  By  William 
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Hispar,  at  the  foot  of  the  longest  glacier  in  the  world  outside  the  polar 
regions  ;  the  first  definitely  recorded  passage  of  the  Hispar  Pass,  the  longest 
known  pass  in  the  world  ;  and  the  ascent  of  Pioneer  Peak  (about  23,000 
feet),  the  highest  ascent  yet  authentically  made.  No  better  man  could  have 
been  chosen  for  this  important  expedition  than  Mr.  Conway,  who  has  spent 
over  twenty  years  in  mountaineering  work  in  the  Alps.  Already  the  author 
of  nine  published  books,  he  has  recorded  his  discoveries  in  this  volume  in  the 
clear,  incisive,  and  thrilling  language  of  an  expert. 

"  It  would  be  hard  to  say  too  much  in  praise  of  this  superb  work.  As  a  record  of 
mountaineering  it  is  almost,  if  not  quite,  unique.  Among  records  of  Himalayan  ex- 
ploration it  certainly  stands  alone.  .  .  .  The  farther  Himalayas  .  .  .  have  never  been 
so  faithfully— in  other  words,  so  poetically — piesented  as  in  the  masterly  delicate 
sketches  with  which  Mr.  McCormick  has  adorned  this  book."— London  Daily  News. 

"This  stately  volume  is  a  worthy  record  of  a  splendid  journey.  .  .  .  The  book  is 
not  merely  the  narrative  of  the  best  organized  and  most  successful  mountaineering  ex- 
pedition as  yet  made;  it  is  a  most  valuable  and  minute  account,  based  on  first-hand 
evidence,  of  a  most  fascinating  region  of  the  heaven-soaring  Himalayas." — Pall  Mall 
Gazette. 

"  .Mr.  Conway's  volume  is  a  splendid  record  of  a  daring  and  adventurous  scientific 
expedition.  .  .  .  What  Mr.  Whymper  did  for  the  Northern  Andes,  Mr.  Conway  has 
done  for  the  Karakorum  Himalayas." — London  Times. 

"  It  would  be  difficult  to  say  which  of  the  many  classes  of  readers  who  will  welcome 
the  work  will  find  most  enjoyment  in  its  fascinating  pages.  Mr.  Conway's  pen  and  Mr. 
McC'irmick's  pencil  have  made  their  countrymen  partners  in  their  pleasure." — London 
Standard. 

"...  In  addition  to  this,  Mr.  Conway  is  a  man  of  letters,  a  student  (and  a  teacher, 
too)  of  art,  a  scholar  in  several  languages;  one,  too,  who  knows  the  Latin  names  ot 
plants,  and  the  use  of  theodolite  and  plane  table.  From  him,  therefore,  if  from  any 
one,  the  world  had  a  right  to  expect  a  book  that  should  combine  accurate  observation 
and  intelligible  reporting  with  an  original  and  acute  record  of  impressions;  nor  will 
the  world  have  any  reason  to  be  disappointed  " — London  Athenaum. 

"  With  its  three  hundred  illustrations  we  have  seldom  seen  a  volume  which  speaks 
to  the  eye  and  understanding  so  pleasantly  and  expressively  on  every  page.  .  .  .  We 
have  an  exhaustive  panorama  of  the  Himalayan  scenery,  of  the  manner  in  which  the 
rough  marching  was  conducted,  of  ascents  achieved  under  the  most  dangerous  condi- 
tions, and  of  the  troubles  and  humors  of  the  shifting  camps  where  the  coolies  rested 
from  their  labors." — London  Saturday  Review. 

"  Perhaps  no  book  of  recent  date  gives  a  simpler  or  at  the  same  time  more  effective 
picture  of  the  truly  wonderful  mountain  regions  lying  behind  the  northern  barrier  of 
India  than  Mr.  Conway's  striking  volume." — London  Telegraph. 


New  York:    D.  APPLETON  &  CO.,  72  Fifth  Avenue. 


D.   APPLETON  &   CO.'S   PUBLICATIONS. 


MODERN    SCIENCE    SERIES. 
Edited' by  Sir  John  Lubbock,  Bart.,  F.  R.  S. 

'JTHE    CA  USE  OF  AN  ICE  AGE.     By  Sir  Robert 
'        Ball,  LL.  D.,  F.  R.  S.,  Royal  Astronomer  of  Ireland  ;  author 
of  "  Siar  Land,"  "  The  Story  of  the  Sun,"  etc. 
"Sir  Robert  Ball's  book  is,  as  a  matter  of  course,  admirably  written.    Though  but  a 
small  one,  it  is  a  most  important  contribution  to  geology." — London  Saturday  Review. 
"  A  fascinating  subject,  cleverly  related  and  almost  colloquially  discussed." — Phila- 
delphia Public  Ledger. 

'THE   HORSE:    A    Study  in    Natural    History.      By 

-*        William  H.  Flower,  C.  B.,  Director  in  the  British  Natural 

History  Museum.     With  27  Illustrations. 

"  The  author  admits  that  there  are  3,800  separate  treatises  on  the  horse  already  pub 

lished.  but  he  thinks  fchjtt  he  can  add  something   to  the  amount  of  useful  information 

now  before  the  public,  and  that  something  not  heretofore  written  will  be  found  in  this 

book.     The  volume  gives  a  large  amount  of  information,  both  scientific  and  practical, 

on  the  noble  animal  of  wh-ch  it  treats." — New  i  'ork  Commercial  Advertiser. 

'THE  OAK:    A  Study  in   Botany.     By  H.  Marshall 

*■        Ward,  F.  R.  S.     With  53  Illustrations. 
"  From  the  acorn  to  the  timber  which  has  figured  so  gloriously  in  English  ships 
and  houses,  the  tree  is  fully  described,  and   all  its  living  and  preserved  beauties  and 
virtues,  in  nature  and  in  construction,  are  recounted  and  pictured." — Brooklyn  Eagle. 

CTHNOLOGY  IN  FOLKLORE.      By  George  L. 
■*- — "    Gomme,  F.  S.  A.,  President  of  the  Folklore  Society,  etc. 

"The  author  puts  forward  no  extravagant  assumptions,  and  the  method  he  points 
out  for  the  comparative  study  of  folklore  seems  to  promise  a  considerable  extension  of 
knowledge  as  to  prehistoric  times." — Indepe7ident. 

pHE    LAWS   AND    PROPERTIES    OF  MAT- 

J-        TER.      By  R.  T.   Glazebrook,   F.  R.  S.,  Fellow   of   Trinity 

College,  Cambridge. 

"  It  is  astonishing  how  interesting  such  a  book  can  be  made  when  the  author  has  a 

perfect  mastery  of  his  subject,  as   Mr.  Glazebrook  has.      One  knows  nothing  of  the 

world  in  which  he  lives  until  he  has  obtained  some  insight  of  the  properties  of  matter 

as  explained  in  this  excellent  work." — Chicago  Herald. 


T 


'HE  FAUNA  OF  THE  DEEP  SEA.  By  Sydney 
J.  HlCKSON,  M.  A.,  Fellow  of  Downing  College,  Cambridge. 
With  23  Illustrations. 
"That  realm  of  mystery  and  wonders  at  the  bottom  of  the  great  waters  is  gradually 
being  mapped  and  explored  and  studied  until  its  secrets  seem  no  longer  secrets.  .  .  . 
This  excellent  book  has  a  score  of  illustrations  and  a  careful  index  to  add  to  its  value, 
and  in  every  way  is  to  be  commended  for  its  interest  and  its  scientific  merit." — Chicago 
Times. 

Each,   i2mo,   cloth,   $1.00. 


New  York  :  D.  APPLETON  &  CO.,  72  Fifth  Avenufc. 


Webster  Family  Library  of  Veterinary  Medicine 
Cummings  School  of  Veterinary  Medicine  at 
Tufts  University 
200  Westboro  Road 
North  Grafton,  MA  01 536 


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